Does anyone know if you can connect to limewire through a network connection?

Yes you can. But it all depends upon where you are, whether there's firewalls you're unaware of, whether there's any p2p filter programs runnng (such as some companies might use), or ports deliberately blocked, or only allowable programs allowed internally or to connect externally. So it does depend.

There's lots of people on networks who use gnutella. Generally their external ip starts with 192. or 10. It's almost impossible to direct connect to people with these ip's. But uplding & downlding from them is generally fine. But that also depends.