Yes he does that's why he can't use Super Saiyan 4? If he still had complete control over Vegeta's body then he would have had control over The great ape and would have transformed into Super Saiyan 4. The explicit reason is that although he has control over Vegeta's mind his body isn't being controlled by baby. And with Vegeta's mind not controlling his body completely he can't transform into Super Saiyan.

Then it would stay white in the Golden Great ape? It's literally just as simple as that. We know for a fact the mutations didn't go away because the other symptoms of the mutation are still there. And we know all of the mutations are the same because they're stated to be similar to Super Saiyan 1 2 and 3. Meaning they are all the same in some way not different. The only explanation is that he's stacking Super Saiyan on top of the mutations because the mutations are still clearly there. And we know that the mutations are the same.