It seems that, after we die, we just detach from the physical body and move on to the barzakh life, which includes questioning in/around the grave by Munkar and Nakir. So we do not lose awareness (or "die") before that happens; we just shed the physical body and possibly move into some type of body appropriate for the barzakh.
Rather, after we have lived in the barzakh, we "die" and are woken up/resurrected for the final judgment, which is not carried out by Munkar and Nakir.
Anyway, we will find out.