Can I make my fish stew recipe into a Chicken Caciatore recipe?
Your tomato-veggie-herb-wine mix is a pretty generic (tomato) sauce base, so replacing the protein would work for more or less every meat, adjusting cooking times etc., of course.

A pollo ciaccatore ("chicken hunter-style") is such a basic dish that there are lots of varieties all over Italy and probably from one household to another. Your base sauce is probably the most simplified one would think of and there is a list of add-ins or changes that are common and work as well: mushrooms, olives, capers, red wine, sometimes even potatoes... And I wouldn't dare to declare one "the right" version here or anywhere.

There are probably two changes I would suggest for your recipe nevertheless:
searing the meat before stewing and adding some garlic.

Otherwise: have fun, I think you can't go wrong with your idea.