Will this be checkmate?


Another one of these threads.
Simple answer: Yes, it is checkmate.
Just because the bishop is pinned doesn't mean that it doesn't still protect the queen from the king. If you let the white king "move into check" by taking the queen, then you also have to let black "move into check" by taking the king with the bishop. Once the white king is dead, the rest of the pieces explode on their spot and are incapable of acting, leaving the black king alive.