As long as the difference between European and "colonial" birth rates is small enough. Without both WWs killing the flower of Europe's youth and imperialism remaining relevant for longer it could be a lot of time.
It is also possible, given these premises, that more Europeans will settle in the colonies, which could lead to more autonomy given them, which could delay independence.
Also if the situation becomes untenable (See Congo.), Empires may end up supporting each other (Or post-colonial Apartheid-like states.), afraid that independent native states would be too much of an inspiration/support for their own colonies. Or some ethnicities could be given "preference" over others in a divide et impera fashion.
I'd say official imperial institutions would be reduced to purely ceremonial stuff (Just to say that the Empire is still there.) while a lot of autonomy would be granted on paper, but in practice neocolonial solutions would be implemented.
If everything goes well for the Empires (And the opposite of well for many others.) this system might be kept for a couple centuries while constantly transforming, opening more and more to colonials as these get more and more integrated in imperial culture and institutions. Some places close enough to Europe might even end up being considered European, given enough time and optimal conditions.
The Ottomans and Russia here represent peculiar situations: the former, without too much foreign interference, can resist rebellions and as soon as it starts exploiting its resources will become fabulously wealthy, the latter will undergo social changes (But probably keep the Tsar.) and enough economic growth to eclipse the Germans someday.