The TV series Bob & Rose written by Russell T Davies is about Bob, very much a gay man, falling in love with Rose, a cis-het woman, while still preserving his gay identity, and how they (and friends and family) process this disparity between identity and behavior.

So the answer is, yes, of course. How we identify ourselves doesn't always match our behavior, and so long as the closet is a necessity, we have to be allowed to have mismatches between identity and behavior.