Yes BA has its own set of check-in desks in PIT, you can't miss them, it's not exactly a large check-in area. I guess they open 4 hours before check-in but for BA services generally you can find out this timing (and the desk location) quite easily in BA's Manage My Booking, either the main website or the App.

In the new layout of MMB select "Go back to Previous Design" on the top of the screen, then expand the PIT - LHR area, then Check In then Other ways to check in then Airport Desks.