Yes it is useful. After the pawn exchange the a file will be open and white could attack black's kingside.
The Process of Decision Making in Chess Volume 2: Practice positions and solutions. Position 1.2

I don't see why black can't exchange. After the exchange black can play a6 and then what for white? Black's rook is better placed. Black also has a bishop vs a knight in an open position.

I think Black's better off if he doesn't exchange. He won't lose his c-pawn. For example, 1... Bc8 2. bxc3 Rc7 3. Nb5 Rxc4 4. Nxa7 Rxc3 5. Nxc8 Rxc8 6. Rb1 Rc7 (Black's position seems better now. Both kings need to get in the game, but Black's rook making it hard for white's king to get across the c-file seems to give Black the winning chances here. )
Here is position 1.2 from volume 2- Goals and Plans , good luck!