uuhhh....no not really, not in this case. There are some restrictions, you can't just do what you like, if that we're the case then next time I'm in the right seat of the 320 I'd prefer to log it as PIC time on a 380, because that tickles my fancy.
There are specific rules regarding in-flight relief, whether relieving or being relieved. Now since I fly the 320 I will not give you the definite answer, but from some circulars at the company what I've seen is that the designated PIC of the flight can log the entire flight as PIC including all time spent at rest. All other pilots on board are only to log time spent at the flight controls. Hope that helps.