A bit of a clarification here: To say you are Asleep is incorrect. I assume that you mean your active Pokemon, correct?
Anyway, yes, you can still play Trainer and Supporter cards even if your active Pokemon is Asleep. The rulebook does not say that you cannot, therefore, it is perfectly legal to play them. In fact, there is not a single special condition in this format that would prevent you from playing them. Trainer cards can be prevented from seeing play, however, the only cards that do so is Kabutops MD, Gastly SF, and Dialga G PL.