What is the maximum practical size of an interferometer? Apart from the obvious fact that this depends on the maximum practical technological capacity any given technological society has at any given time, then the correct answer is it depends.
However, it worth considering what constitutes Very Long Baseline Interferometry (VLBI) and try to dtermine whether it is workable in the OP's scenario.
VLBI is an acronym for Very Long Baseline Interferometry and associated with radio astronomy and geodesy. Typically VLBI refers to
experiments that do not process their data in real time, but record it
for later correlation. In the world of increasing network
connectivity, we are entering the realm of eVLBI (electronic VLBI), in
which data are cross correlated in virtually real time. VLBI
experiments have baselines of usually 100s or 1000s of km.
VLBI falls into several categories:
Continental – baselines of 100s to 1000s of km,
Global – Baselines of 1000s of km,
Space VLBI – involving the use of satellites, like VSOP.
VLBI is used in measuring pulsar parallaxes and proper motions,
resolving the cores of radio galaxies and jets from supermassive black
holes, among others.
The real question is whether "data are cross correlated in virtually real time" means that if data can be cross correlated using FTL spacecraft to transport data sets to combined and analyzed at a given node in the system, then this interstellar baseline interferometer is a practical working system.
Having multiple telescopes located in multiple planetary systems, while this might be convenient, doesn't seem like a good idea. The various interferometer component dishes would be better located in space, outside planetary systems to minimize gravitational perturbations, and with this elements are relative rest to each other. This is basically how space-based VBLI systems currently work. The same principles should apply not over interstellar distances.
Essentially the cross correlation centre should be located at the midpoint of the various interferometer telescopes, so that the data are analyzed as if it was part of the one single array. This won't be analyzing the data in "true" real time, but in a "time-shifted" virtual real-time.
Referring back to the basic principles of radio astronomy interferometry and this give a reasonable idea of the practically of an interferometer VLBI and its effective resolution of stars hundreds of light years distant.
A radio interferometer is an array of radio antennas or ‘elements’
that are used in astronomical observations simultaneously to simulate
a discretely-sampled single telescope of very large aperture. To put
it another way, a radio interferometer can be thought of as a single
telescope with a very large and incompletely-filled aperture, of
maximum size equivalent to the maximum spacing, or baseline, between
any two of its component elements. This large ‘synthesized’ aperture
is only sampled at the locations at which an element exists, and this
is aided by the rotation of the Earth which effectively moves the
elements within it, hence increasing the sampling. This is known as
‘Earth rotation aperture synthesis’. The size of the synthesized
aperture dictates the resolution or ‘beam size’ of the array; the
larger the aperture, the smaller the resolution.
Source: radio interferometer
If the aperture size is light years, then the resolution of stars hundreds of light years away should be extremely good. Certainly, enough to map the surfaces of any planets.