The Swedish Homestead YT channel shows pigs and
chickens working in a
greenhouse, without plants.
Joel Salatin does something similar with
chickens and
rabbits.
No plants, but warm animals in an un-insulated space, doing quite well.
Cows make a lot more methane, but I think it could be managed.
Compost pile heating of a hoophouse is a thing, so having a steady supply of compostables being created could also be a thing.
Keeping the fresh turds mixed with carbonous material could be a lot of work, if we did it our selves.
But we could assign that duty to some
chickens, or to a couple of pigs, or some of both.
It's getting kind crowded in the hoop house at this point, and that might be the real drawback of this idea.
Making room for plants and animals, and keeping the animals from destroying the plants, could be a challenge.
At my own home I'm trying to build a green house with provisions for chickens to come visit.
By provisions, I mean things that keep them from wrecking the plants.
This will probably consist of curtains made of mesh and weighted at the bottom.