No, stockfish uses minimax with pruning. Minimax and MCTS are just different algorithms.

Does Stockfish use Alpha Beta pruning?

Nonetheless, the classical chess search algorithm is exhaustive. Breadth-first search with Alpha-Beta pruning is how it is taught at universities. Stockfish uses iterated deepening as you've said, but that's very similar to Breadth-first search.

Does Stockfish use neural networks?

To recap, Stockfish evaluates about 100 million positions per second using rudimentary heuristics, whereas Leela Chess evaluates 40 000 positions per second using a deep neural network trained from millions of games of self-play. ...