The first answer is you can and should log all the flying you do. Whether people will count it towards future things is the question.
As long as you can show that the company ops manual has procedures for multi pilot operation then most , if not all, NAAs will accept that as P2 time the same as if it were on an AOC. However as far as i am aware this is not written anywhere, the regulations only mention it where a single pilot aircraft is being flown muti pilot due the ops regulations.