The FP machines have no way of knowing which park an individual is at, or if the individual is even in a particular park.
(They do not scan passes when people leave parks, only when they enter, and at this point, the only requirement for FP is that the pass has to have been initialized on that particular day in order to work. A pass is initialized by having the pass holder go through an entry gate and officially enter the park by having the pass scanned.)
So, if the entire party gets up in the morning, enters either park, and then everyone goes back to the hotel except for a runner, that runner could go back and forth collecting FP as much as they wanted, and then hook up with the group.
I give that as an extreme example, but people do do that, FWIW, if there are a couple young energetic members of the group that can be trusted with the passes, it's a good way to get some extra pool time while also getting FP for later, if the younger folks are hell bent on going in for the morning session, join them, get through the line into the park, give them your initialized pass, and then leave (making sure to get a hand stamp for reentry).
