They eat a lot of it in Kentucky, where it's a barbecue staple. PQM does mutton BBQ sandwiches here in Chicago occasionally.
I'd say that mutton and burgoo are the defining elements of Kentucky BBQ.
Unrelated humor: I searched "pqm bbq chicago" on duckduckgo.com and on the map, just west of PQM there's a marker for "Duck Duck Goat" :D