Sure, but shop sounds nicer, doesn't it? Kind of like the bar isn't just a "hang out at Carol's house" and Barton's coffee shop isn't just "let's go drink Clint's coffee because he made too much."
I don't see why not. It's doable, and at least most of the vegetables you could get straight from the gardens so you wouldn't have to ... scavenge as much. Plus it'd take up some of your time and it benefits the rest of the town. It's a great idea.