Definitely. The more white people you have, the longer it'll take to overthrow them. At some point there'll be a critical mass point (I don't know what point - perhaps about 30% compared to IOTL's 10%?) where sheer numbers will make it very difficult if not impossible to overthrow them - a well trained and equipped paramilitary "race police" could easily keep down several times its number of disorganized revolutionaries. Such large numbers may even reduce white paranoia and prevent apartheid proper from being instituted, relying on something more like Jim Crow. With careful media and political control, they may even be able to give non-whites the vote and still maintain almost complete power.
Eventually, liberalization of the white populace will probably see more and more power slowly ceded to everyone else, but that could well take generations.