All passes have to be activated in at least one of the parks...meaning that if you all go to DCA and one person goes to DL for a FP for everyone, they can collect FP. However, if you are talking about some of the group hanging back at the hotel while one person goes to the park to get a FP, they will not be able to do that since the tickets have not been activated in one of the parks.
Hope that makes sense.
Now that I have re-read your question, it sounds like your question is more in line with my second scenario, so the answer would be No.