Very far-fetched.
The main challenge of placing living beings in space is pressure containment. Zero pressure outside means that everything will evaporate, sublimate, or find some way, any way, to escape. Even conventional plastics can't survive in space due to outgassing.
The process of photosynthesis requires oxygen and water (separately or dissolved). These will have to be contained entirely inside the plant.
But not impossible.
First, let's get the first thing out: there is almost no way for such lifeforms to evolve naturally. You need air and water, which require pressure, to begin evolution.
This calls for genetic engineering beyond our current dreams. We're talking the ability to completely design a being's behavior, from scratch. You're no longer constrained by such categories as "plant" or "animal"; you're the master of life.
Let's make it clear what this level of biotech entails. By this time, your species has long overcome death from age and disease. Your children's characteristics are freely defined by their creators. Maybe "parents", but all except the most hardcore of primitivists aren't wasting their bodies on childbirth. In fact, the only reason you're not engineering photosynthesis right into your species is that it just isn't efficient for a highly mobile being.
The actual design
The plant-creature will have to build an impermeable protective shell, acting as a pressure vessel, containing the air and water inside.
We already know of such shells. Chitin carapaces and nails are reasonably impermeable. These shells grow slower than normal cells, but they do grow.
This space plant will most likely grow in thick tubes, which circulate the fluids and gases on the inside, and have a transparent outer shell. Thickness is needed for a phase-change capillary circulation route: gas goes one way, liquid through capillaries the other, similar to a heatpipe. These tubes will grow and spread, probably looking like a green glossy growths from the outside.
Of course, photosynthesis will only work if you're reasonably close to a star. Otherwise, you'll have to light them up with artificial lighting. In which case...
There's an easier option
Yes, the "frame challenge" so popular here.
Photosynthesis doesn't require land plants. It can be performed by phytoplankton even better. So - just make tubes and fill them with a hydroponic liquid, complete with the phytoplankton. Plastic can be transported as big bricks, melted down, extruded, welded. And these tubes can use forced circulation. They'll be resilient to damage, because you can have billions of loops, where losing just a few is a non-issue. All you need is lots of water.
Greenhouses are for haute cuisine delicacies. Tomatoes that look and taste Earth-grown. Sliced to the thinnest of the possibilities, and decorated with 0.1 mm sheets of radish. The luxuries of the space elites.
FOOD is the phytoplankton-based green goo. It's a monotonous diet, but artificial flavorings, dyes, and baking techniques can make anything look, feel and taste like something else. We rarely eat it today, because it's difficult to extract out of its water habitat, but we do eat it.
It's got a strong marine flavor, compared to lobster heads, and is considered a delicacy. Plankton been studied as a source of human food, found quite healthy, if a bit heavy on proteins. But much harder to filter out of a large volume of seawater than just catching the fish. That changes in space, where other foods are so much less accessible that plankton might just win on price.
...Will it taste like chicken?
Space-adapted plants won't be particularly tender, since they have to survive space. You're looking at a plastic-like outer shell, with layers of tough connective tissue underneath, needed for thermal insulation. All of that transparent, but with an airy photosynthesis tissue on the inside, and little room for any "fruit-like" formations. They'll likely be closer to the green goo, needing processing for human consumption.
But yes, it can taste like chicken, if you engineer chicken flavoring into its DNA. Just, without thorough processing, not one worthy of a civil war colonel.
