Network Screen Saver without locking up the desktop

We are a High School and have implemented a Screen Saver GPO that locks the computers after 11 minutes. This is causing a issue with teaching in some classrooms. I have one admin that is asking if there is a way to lock the teachers out of the network programs but not the desktop instead. I have told him no because when they log into the computer they are logging into the computer and network. I thought I would throw this out to see if someone has a creative way to do this?