Is it possible to use Unity Multiplayer Networking

Yes. That has nothing to do with building to GearVR.

What all is needed to start any kind of networking? I am super new to this world, and I am wondering where I should start. With Oculus Platform tools, I'm guessing I still need a server service of some sort (like Photon)? Does Oculus have some kind of server that we can build off of?