Yes but wait until the fake tan has sunk in, which means a wait of about 10mins.
The best time to apply the fake tan, is in the evening, so you wont need to put anything on top of it and then you can then also sleep with it intact.
In the am, you can wash any residue off. It also means that you wont have to spend the day with the "fake tan" smell whafting about your nose!!