Former Italian sport historian here. It is true, but it is often misunderstood outside Italy. It's just a pretty rough war-like generic encouragement, not a menace: "vincere o morire" (to win or to die) is in the infinite form of both verbs; "o vincete o morite" (you win or you die) would have properly been what non-Italians usually think it meant.

Edit: so no, it didn't affect anything, at least not in the proportions you may think. I remember a player taking about it and how it was perceived as a typical fascist strong encouragement, very appreciated by the players.