Is it possible to make network connections in the editor? I'm curious to know if it is possible to setup a server -> client connection that will allow multiple people to work in a single level.
If you mean pressing Play in the editor and having the game create a connection - definitely yes. You can even open two instances of the editor and debug a game that way (One instance is the server, one is the client).
If you mean you want to create some kind of connection between the editors while you're editing a level - and not in play mode - I don't think there's anything that can stop you. It's just that it would be a real hassle to debug. I imagine it can be some kind of editor script.
Of course I haven't even actually tried opening a socket from an editor script, so I might be missing something, but I can't see why you couldn't.