Of course, but not with Monte Carlo tree search. https://en.wikipedia.org/wiki/Monte_Carlo_tree_search It is a heuristic that does not converge to the perfect game.

Yes, it does, if you think about how it works, it converges on perfect play, and your link says so: "it has been proven that the evaluation of moves in MCTS converges to the minimax evaluation" ("with “average” back-up and UCT move selection, the root evaluation converges to the “min-max” evaluation when the number of simulations goes to infinity").

Well - a Monte Carlo tree search consist of two parts. The tree search and a Monte Carlo simulation. A tree is build up until a certain point. Now this nodes are evaluated by a monte carlo simulation where stones are placed randomly until the board could be evaluated. Now we have two options to spend additional computer power. Expanding the tree search and/or expanding the monte carlo simulation. If we expand the tree search to all the leaves of the game tree we basically end up with a min/max approach since the monte Carlo simulation part is not necessary. However, if you use the additional computing power on more monte carlo simulations it does not converge always.

The part your cited is only true for games with random turn order - that is obv. not the case for Go.

"It converges to perfect play (as k tends to infinity) in board filling games with random turn order, for instance in Hex with random turn order"