Suppose the game allows the king to be captured (since checkmate technically results in a king being captured next move).
What happens if this occurs?
If Black captures Kxg7, the bishop can capture the king on g7 before the queen on b5 can capture the king on b1.
So yes, a pinned piece can still somewhat protect another piece so that this other piece cannot be effectively captured by the opposing king.
This sounds very similar to a question I posted here years ago - How can a PINNED PIECE (pinned to king) have influence over squares it can't even LEGALLY move to? Such as a pinned bishop preventing the opponent from castling?
After a long (and pointless) discussion, one intelligent person finally posted a diagram illustrating how convoluted positions could become if that was the case. Wish I could remember the exact diagram posted, but it made total sense. The game would become completely convoluted with various pinned pieces and trying to figure out which pieces actually had influence over which squares.
Should pinned pieces be able to check or defend checking pieces? They can't take back.