Narita is pretty good at sending priority bags first up the conveyor belt. I have a resident alien card for japan and rarely spend more than 5 minutes in immigration; to my amazement my bags are often on the belt waiting right after clearing immigration (and that seems to be true not only for first class luggage but also for priority luggage).

In general the immigration line at narita can be so bad (it's not uncommon to spend 30 minutes waiting in line) for non residents and citizens that all bags sometimes makes it onto the belt before you even get to the customs area.