Chicken places in my area deliver through 3rd parties and it is a less than stellar experience.
My pizzeria uses its own in-house drivers. If I served chicken of equal quality to “chicken only” stores, will the prospect of reliable and less expensive delivery outweigh the branding issue of getting chicken from a pizza place?
I feel pizza and wings are starting to be kinda synonymous. So yeah I see no reason why you wouldn’t be able to take a chunk of the pie. In my experience people order by taste and budget and also what’s most convenient so if you can offer a better ordering and delivery experience I think you could do well.
Do it as a Ghost Kitchen. Separate brand for chicken, unique website URL, and a dedicated phone line answered “MSG Chicken”. The only people that would know are those that come in for pick up; tell them, “it’s one of those new ghost kitchens you’ve been hearing so much about using our extra space to get started.”