The problem with any such scenario is that European colonisation happened because of very specific combination of geographic, economic, diplomatic, technologic, sociologic and even relegious reasons. Those are very hard to replicate in other parts of the world. I am not saying that Europe is destined to rule the world. Quite the opposite. Europe was very lucky. it got what it It had just the right circumstances at the right time. Personaly I doubt that if for examplethe Roman Empire had survived Europe would have been so succesful colinising the world. If North Africa hadn't become Islamic, Europe wouldn't have been as succesful, etc.
In the end colonisation happened more or less by accident. Basicly what the Europeans wanted was to trade directly with Asia and that is why they managed to colonise the world. In asia money was to be made and the Europeans invested a lot to get that money, including funding Columbus' terrible idea. Colonisation of the Americas was so succesful, because the natives died so quickly because of the diseases, leaving easy open land for the Europeans. Africa was more or less ignored for centuries, because there was nothing to get in Africa. Even African slaves were the third choice for Europeans (using native Americans and Europeans failed, thus the third choice was to get the Africans).
All this is very hard to replicate for the Asians. There is no incentive for them to go to Europe or Africa (too little to gain). The Americas would be an option, if geography isn't against them. Crossing the Pacific from Asia is a lot harder than crossing the Atlantic from Europe.
So in the end, no I don't think it will happen. Asia can still dominate the world, of course. Technologically and socialy they were on par with Europe. So they could have, just like the Europeans did. They just would do it very differently than the Europeans did.