Well, I suppose Pyotr III would've continued to bumble on as he did. But the truth is, he pissed off a lot of people, so he probably would've been overthrown anyway (whether by his wife, that Anhalter princess or the nobility in a Time of Troubles 2.0). Also it means that Russia would've stayed in the pro-Austrian camp longer and that it would've taken another generation or two before Russia could successfully build dynastic ties to the rest of Western Europe