Humankind would become one mono-race.
Only if that randofucking continued. If it didn't, if these mono-race people settled into communities and generally bred locally, then local conditions such as sunlight and diet would once again begin to create evolutionary diversity.

Also, how does randofucking ever actually happen? You have to first of all mix the population thoroughly, then overcome any racial problems that might exist so there's a genuine random element to the fucking when looked at as a large sample. Then you have to keep people moving, keep the monos (is that a raicst term in this world?) from getting too much, or too little, sunlight.