I very much doubt that. Of course, there is no alternative reality where you could observe how things went when things were done differently, but there's no lack of violence in parts of the world where US and EU have not been doing things.

And of course you are neglecting that especially after WWII, Soviet Union did not exactly stay out of places, either. For instance, Afghanistan and Somalia, the two most notorious failed states in the world, were actually run under Soviet influence for a considerable time. Syria is still very much in the Russian sphere of influence. Etc.