Maybe not impossible, but...
There are several competing, opposed requirements here:
- Minimise balloon mass and leakage area - in order to enclose a given volume, the ideal shape to minimise surface area (and therefore "balloon fabric") is a sphere.
- Maximise photosynthesis and mineral collection - this requires as much surface area as possible, which is... not a sphere. There are very few spherical plants in nature, most have leaves and structures to spread out leaves. The ones that are closest to being a sphere are some cacti, which have that shape in order to minimise moisture loss...
- Survive hostile biomes - a plant that floats along at the mercy of the wind is going to go places. Single-biome planets are impossible due to basic physics, which in turn means that the plant will float to less-than-ideal biomes for the plant, where it needs to conserve moisture and/or warmth. This is a problem, because a plant that is as light as possible in order to float does not have the weight allowance to have spare water or insulation. The result is that sooner or later the plant will die by being frozen or dehydrated or both.
Some plants survive hostile environments by growing and reproducing really, really quickly - even though many die, there are enough to keep the species going. However, this type of plant cannot grow quickly - it has insufficient surface area to get the surplus energy from photosynthesis for rapid growth and it has insufficient raw materials from suspended minerals in the air to grow even if it did have the energy. (Remember that suspended minerals in the vicinity of the plant are floating through the air in the same direction at the same speed, so it will not be able to gather much material at all. A filter feeder collecting material suspended in a fluid must move at a different speed than the fluid, eg be fixed to the ground as the fluid flows past.) As for water - the amount of precipitation and/or humidity will vary constantly depending on what biome the plant is floating through and what the weather is like at that location at that time.
In summary, I cannot see how this kind of plant could survive.
Note that this answer is not even examining the following issues:
- genetic diversity of plant species that only reproduces asexually.
- how to create lighter gases within the "balloon", as this has been explored elsewhere repeatedly.
- effects of aerial creatures grazing on the plants that are easily spotted floating through the air.