Not necassaraly, his heir (probably) wouldn't have had the ability as a general that Ghengis had, evan if he had there had all ready been European leaders that had proven their ability at fighting people with similar tactics of Ghengis and so he may have started to lose. You cannot say for sure that he would have taken Europe.
Evan if he had his empire wouldn't have taken long to collapse, it was too big with too many differant races, and no empire of great size ever survived past its initial leader (bar The British). His empires collapse was inevitable heir or not