Yes, the online hardware used during the game, vs. the offline hardware used for training the neural network, is mainly there to run a ton of monte carlo tree search (MCTS) iterations. MCTS tends to produce better estimates as you throw more compute power at it. In perfect-information, deterministic games, it theoretically converges on optimal play given infinite compute power, although in games with very large state spaces in practice that guarantee isn't too useful on its own, and the heuristic guidance provided by the NN is crucial.