Whe you log off your computer to the user screen does the Internet disconnect. So if you were downloading files would that pause or continue to download when you log off your computer to the user screen?
Any applications utilizing the internet while running under your user account would be terminated, however the internet connection to the PC would still be on. Anything running as a service would still be running.
I'm not sure if your p2p program runs as a service but I doubt it. It probably gets killed when you log off. If you want to see a list of all services type services.msc into your search box. Most of them are part of your OS.