It is unlikely that the Mongols would have been successful in attacking the Holy Roman Empire in the long run, let's not forget that Europe was recovering from years of crusade and Pope Gregory (I forget which number) called crusade against the Mongols shortly before Subotai withdrew forcing Batu to withdraw with him.
Also it after the uniting figures of Genghis and Subutai passed the Empire fell inward on itself.
It would have been interesting though to see what would have happened, considering the Christian Soldiers of the vastly superior northern European Nations (as compared to the Eastern European Nations) were as blood thirsty and fervent as the Mongols ever were. Still if they had overrun Europe an entirely Islamic world might have been a little more peaceful......
I was really referring to after the 1400's however and the spread of European Influence (especially the Spanish, Portuguese and British) globally. (I'll be more precise in future...)
I'll let you off for mistaking 600 years with 2000 then just this once
