Unlikely. We have yet to master nutrition when it comes from plants, it will be even worse for a bioreactor. Unfortunately, the list of food ingredients that you see listed in minimum recommended intake values is woefully incomplete. There's a whole bunch of micronutrients we get from food that are difficult to replicate.
Bioreactors could be useful for making supplements (say, Omega-3) to offset specific deficiencies.
If we are to eat just processed food in space, we'll need a lot more research on this. It would be better if we just grew food from plants.
The problem is not finding food that is still edible after years in storage, but food that the crew can eat long term without getting sick and without developing deficiency diseases. For example, the Pentagon says you can't eat MREs for longer than 21 consecutive days.
The space food problem is genuinely hard and interesting, you can get a sense of it in this paper: https://www.sciencedirect.com/science/article/pii/S221455242...