Yes. That's why MPAA has no way to see you are downloading their movies if you are part of a closed invite-only video downloading network. Though there is a chance that someone from the MPAA would get themselves invited in that community and sue everyone inside, I don't think MPAA cares to sue the relatively small amount of users in closed communities.
Once there is a p2p software that sends a file from one internet adress to another one, MPAA can thus always sniff the connection.
Unless the p2p software is set-up to use part of some proxy connections and part of direct connections, and if everyone uses that software, this way MPAA would have no way to sue people for just serving as proxy to others p2p activity, and they'd have no way to prove that any specific person is actually "pirating" the content.
Anyways, it is an impossible thing for MPAA, IFPI or any government to fight p2p "piracy". Thus their only chance is eigther to improve their content value, and completely change their business model, for example sell all their movies same day as theatre release for 1$ per download or some low price like that. But most probably that MPAA and IFPI and all the movie and music majors will soon be out of business, and that the winner will in the end be the artists and the consumers.