Rolling pick-up: rolling as in a rolling meet. The train slows down to walking speed (4mph or less), the conductor, engineer, and brakeman and/or fireman (if applicable) get on the equipment without the train even stopping.
Amtrak probably doesn't allow it (I think BNSF doesn't, either), but getting on and off moving equipment was a regular part of my job on the Alaska Railroad. We did it a couple times when picking up an outlawing train--we got on and took over while the train sped away from the meet. Not sure why we did this instead of stopping and letting the going-dead crew off (maybe there was a time crunch--rolling changeovers take much less time, as otherwise the train is stopped for usually about 5-10 minutes while the new conductor has to call the dispatcher and verify the track bulletins and train's authority), since the outlawing crew stayed on the train (usually moving to the rear unit or, in the case of a passenger train, to the passenger coaches) and therefore earned overtime (they're paid until they arrive at the terminal).
I'm not sure this would be terribly easy (or safe) with the ladder and door of an Amtrak P42 (it's much easier with a freight engine, which has steps near track-level and a deck wrapping around the hood), so it probably isn't done.
gswager: as mentioned above by a few people, I think the hypothetical would almost never come to pass. However, in the case you mention, I would assume the freight conductor would likely not want to deal with passengers (there's usually a reason freight crews work on freight railroads...) and would let the OBS staff handle everything. He'd most likely stay up in the engine (when our three-man crew relieved a passenger train, all three of us stayed up front). Of course, the on-duty conductor is completely in charge of the train, so he could legally do whatever he wanted within the rules of operation and laws governing rail transportation. But again, I don't think this would ever happen unless Amtrak were in truly dire straits--Amtrak wouldn't let non-Amtrak employees handle an Amtrak train for multiple reasons, but a big one would be that non-Amtrak employees aren't checked out on Amtrak's rules and procedures. Another one would probably be union rules--Amtrak's employees probably wouldn't be happy with outside employees taking their jobs.
In one instance where we dog-caught a passenger train, the Suburban that dropped us off picked up the engineer and fireman but left the conductor and brakeman in the back. As long as they weren't doing anything relating to the movement of the train, they were perfectly legal to remain on the clock and help with the passengers. Although by the time we picked them up, there were no more station stops and so no reason for them to deal with "official" duties like checking tickets, they stayed back there (probably mostly relaxing in the work room or staff break room) for the rest of the two-hour trip to Fairbanks.
A question for some more knowledgeable: on occasion, I have seen a freight engine or two on the front of an Amtrak train to help out when, say, Amtrak power dies en-route and replacement power is a long way away. While in a case like this, there is probably a legal Amtrak crew on-board (one that's not dead), I assume a freight engineer would be operating the controls of the locomotive. Who would be in charge? Would the freight engineer be under the direction of the Amtrak conductor, or would the Amtrak crew take a back seat (maybe even literally) to the freight conductor and simply advise him on things like station stops?