Yes, it is Possible
Here are some examples:

from: https://en.wikipedia.org/wiki/Tree_shaping

from: https://www.permaculture.co.uk/articles/artful-science-tree-shaping
I will try to copy-paste some words here, maybe it can help, since I am not knowledgeable about it myself.
Summary
Tree shaping uses living trees and other woody plants as the medium to create structures
and art. There are a few different methods2 [...] such as pleaching,
bonsai, espalier, and topiary, [...]
Most artists use grafting to deliberately induce the inosculation of
living trunks, branches, and roots, into artistic designs or
functional structures.
Inosculation and Living Root Houses and Bridges
Some species of trees exhibit a botanical phenomenon known as
inosculation (or self-grafting) [they] are called inosculate
trees.3
The living root bridges of Cherrapunji, Laitkynsew, and Nongriat, in
the present-day Meghalaya state of northeast India are examples of
tree shaping. These suspension bridges are handmade from the aerial
roots of living banyan fig trees, such as the rubber tree.4 The
pliable tree roots are gradually shaped to grow across a gap, weaving
in sticks, stones, and other inclusions, until they take root on the
other side.4 This process can take up to fifteen years to
complete.[5] There are specimens spanning over 100 feet, some can hold
up to the weight of 50 people.[6][7] The useful lifespan of the
bridges, once complete, is thought to be 500–600 years. They are
naturally self-renewing and self-strengthening as the component roots
grow thicker.[7][8]
Living trees were used to create garden houses in the Middle East, a
practice which later spread to Europe. In Cobham, Kent there are
accounts of a three-story house that could hold 50 people.[9]
Pleaching
Pleaching is a technique used in the very old horticultural practice
of hedge laying. Pleaching consists of first plashing living branches
and twigs and then weaving them together to promote their
inosculation. [...] useful
implementations include fences, lattices, roofs, and walls.[3][10]
Some of the outcomes of pleaching can be considered an early form of
what is known today as tree shaping.
In an early,
labor-intensive, practical use of pleaching in medieval Europe, trees
were installed in the ground in parallel hedgerow lines or quincunx
patterns, then shaped by trimming to form a flat-plane grid above
ground level. When the trees' branches in this grid met those of
neighboring trees, they were grafted together. Once the network of
joints were of substantial size, builders laid planks across the grid,
upon which they built huts to live in, thus keeping the human
settlement safe in times of annual flooding.3 Wooden dancing
platforms were also built and the living tree branch grid bore the
weight of the platform and dancers.[11]
In late medieval European gardens through the 18th century, pleached
allées, interwoven canopies of tree-lined garden avenues, were common.
Methods
There are various methods of shaping a tree.[2][12] Some of
these processes are still experimental,[13]:154 whereas others are
still in the research stage.[14] These methods use a variety of
horticultural and arboricultural techniques to achieve an intended
design. Chairs, tables, living spaces and art may be shaped from
growing trees. [Some techniques used are unique to a particular
practice, whereas other techniques are common to all].
These methods usually
start with an idea of the intended outcome. Some practitioners start
with detailed drawings[15]:7 or designs.[16] Other artists start with
what the tree already has.[17] :56–57 Each process has its own time
frame and a different level of involvement from the tree shaper. The
trees might then either remain growing, as with the living Pooktre
garden chair, or perhaps be harvested as a finished work, like John
Krubsack's chair.
Aeroponics
In 1957, F. W. Went described "the process of growing
plants with air-suspended roots and applying a nutrient mist to the
root section", and in it he coined the word 'aeroponics' to describe
that process. In 2008, root researcher and craftsman Ezekiel Golan
described and secured a patent for a process which allows the roots of
some aeroponically grown woody plants to lengthen and thicken while
still remaining flexible. At lengths of perhaps 6 metres (20 ft) or
more, the soft roots can be formed into pre-determined shapes which
will continue thickening after the shapes are formed and as they
continue to grow.[12][21] Newer techniques and applications, such as
eco-architecture, may allow architects to design, grow, and form large
permanent structures, such as homes, by shaping aeroponically grown
plants and their roots.[14]
Instant Tree Shaping
Instant tree shaping[12][22] starts with mature trees,[23] :53 perhaps
6–12 ft. (2–3.6 m) long[13]:196 and 3-4in (7.6–10 cm) in trunk
diameter,[13]:172 which are bent and woven into the desired design
[23] :53 and held until cast.[24][25] Understanding a tree's fluid
dynamics is important to achieving the desired result.[2][17]:69
Bending is sometimes used to achieve a design.[17] If a plant's tissue
is bent at too sharp an angle it may break, which can be mostly
avoided by un-localizing the bend. This is achieved by making small
bends along the curve of the tree. Bends are then held in place for
several years until their form is permanently cast.[17]:80 The tree's
rate of growth determines the time necessary to overcome its
resistance to the initial bending.[13]:178 The work of bending and
securing in this way might be accomplished in an hour or perhaps in an
afternoon depending on the design.[22]
Ring barking is sometimes employed to help balance a design by slowing
the growth of too-vigorous branches or stopping the growth of
inopportunely placed branches, using different degrees of ring
barking, from simple scoring to complete removal of a 3/8"-wide (1 cm)
band of bark.[17]:57, 69
Creasing is folding trees such as willow and poplar over upon
themselves, creating a right angle. This method is more radical than
bending.[13]:80
With this method it is possible to perform initial bending and
grafting on a project in an hour, as with Peace in Cherry by Richard
Reames,[13]:193[17]:56–57 removing supports in as little as a year and
following up with minimal pruning thereafter.[26]
Gradual tree shaping
Gradual tree shaping starts with designing and
framing.[22][27][28][29] These are fundamental to the success of the
piece.[28][29] Once these are set up, young seedlings or
saplings[15]:4 3–12 in. (7.6–30.5 cm) long[28][29] are planted.
The training starts with young seedlings, saplings or the stems of
trees when they are very young,[15] :4 which are gradually shaped
while the tree is growing to form the desired shape.[9] There is a
small area just behind the growing tip that forms the final
shape.[27][30] The shaping zone,[27][30] it is the shaping of this
area requires day to day or weekly guiding of the new growth. The
growth is guided along predetermined design pathways;[23] this may be
a wooden jig [9] or complex wire design.[16]
With this method the time frame is longer than the other methods. A
chair design might take 8 to 10 years to reach maturity[23][31] Some
of Axel Erlandson trees's took as long as 40 years to assume their
finished shapes.[32]
Framing may be used for various purposes and might consist of any one
or a combination of several materials, such as timber, steel, hollowed
out trees,[6] complex wire designs,[16] wooden jigs,[9] or the tree
itself, living [13]:178 or dead.[33]:58 It can be used in many project
designs to support grafted joints until the grafts are
well-established. Some processes might employ framing to hold a shape
created by bending or fletching mature trees until the tissues have
overcome their resistance to the initial bending and grown enough
annual rings to cast the design permanently.[13] Others might use
framing to support and shape the growth of young saplings [23][30][34]
until they are strong enough to maintain an intended shape without
support.[30] Still other approaches might employ frames to guide the
roots of aeroponically grown trees into desired shapes.
Grafting
Grafting is a commonly employed technique that exploits the natural
biological process of inosculation. A branch or plant is cut and a
piece of another plant is added and held in place. Various types of
grafting all share the goal of encouraging the tissues of one plant to
fuse with those of another.
Grafting is applied to create permanent connections and joints.[23] In
some cases, trees are grafted while they are growing, [35] while in
other cases, mature trees may be intertwined and the stems of two or
more trees are then grafted together to create chairs, ladders, and
other fanciful sculptures.[36]
Pruning
Pruning can be used to balance a design by controlling and directing
growth into a desired shape.[30][33]:70 [34] Pruning above a leaf node
can steer plant growth in the direction of the natural placement of
that leaf bud.[13] Pruning may also be used to keep a design free of
unwanted branches and to reduce canopy size.[30][34] Pruning is
sometimes the only technique used to craft a project.
Trees repeatedly subjected to hard pruning may
experience stunted growth, and some trees may not survive this
treatment.
Using time as part of the construction is intrinsical to achieving
this art form.
Structure
Living grown structures have a number of structural mechanical
advantages over those constructed of lumber[citation needed] and are
more resistant to decay. While there are some decay organisms that can
rot live wood from the outside, and though living trees can carry
decayed and decaying heartwood inside them; in general, living trees
decay from the inside out and dead wood decays from the outside
in.[38] Living wood tissue, particularly sapwood, wields a very potent
defense against decay from either direction, known as
compartmentalization. This protection applies to living trees only and
varies among species.
Growing structures is not as easy as it would seem.[39] Quick growing
willows have been used to grow building structures, they provide
support or protection.[39] A young group of German architects are in
the process of such a structure and they are continually monitored and
checked.[39] Once the trees are of age to be able to take on
load-bearing weight they are tested for stability and strength by a
structural engineer.[39] Once this is approved the supporting
framework is removed.[39] Projects are limited to the trees' weight
loading ability and growth.[39] This is being studied and the load
capacity will be proved by testing on prototypes.[40]
Images
here several image for house

from: http://facebook-tweet.blogspot.com/2011/04/fascinating-living-growing-architecture.html

from: https://imgur.com/gallery/ouAUx/comment/1299310169