I attended BCs BBQ on Easter Sunday in 1999 and noticed they had it in 2002. I think its likely it will be going on. Drinks are available during the Easter holidays except for Good Friday when you have to wait til 6PM.
I'm sure that the only time BCs is closed for business is when the law says so. I believe that's only when the polls are open, a portion of Good Friday and I guess in times of Marshal Law (always have a back door in that case).