Is it absolute that they lose? Of course not. Does it become very plausible because now the US has to use to substitute to replace a lost defenseman and therefore loses an offensive player and in so doing significantly hampers their own scoring opportunities? Certainly. Is there any way of predicting how that decision would have altered the momentum of the game? No.
But at the end of the day, it comes back to what I said before. Given the choice if you want to win, would you rather play a man up or a man down against an evenly matched team in the semifinals of the world's biggest tournament? That answer substantiates my supposition.