I'm saying no because the strength of the sandwich is its simplicity. It doesn't need cheese or BBQ sauce or bacon.
I'd like one tossed in buffalo sauce with some BC crumbles on it... or with swiss cheese, a slice of ham and maybe a dijon mustard (cordon bleu style) don't care for the BBQ sauce really, but cheese and bacon probably wouldn't hurt... maybe the bacon cheese one with some kind of peppercorn ranch or something