If I were to get a game that had multiplayer in it's original version would the GOG version still support the multiplayer?

Usually, yes. Any functionality available in the original game is also present in the GoG editions.
However, if a game depends on something from the developer, for example a serverlist, and the developer doesn't supply it anymore, there could be issues.
AFAIK, the above scenario doesn't apply to any game available on GoG so far, but if you want to be really sure, you should tell us what game you're thinking of, so somebody could confirm it.

If not, you can always try something like to play on a virtual LAN with a friend, or [url=http://www.gameranger.com/]GameRanger, or even the big name multiplayer programs like GameSpy Arcade, and play there.

You'd probably have trouble finding auto-match games for most of the older titles here but if you know people with the game then setting up a session yourself should work nicely

OK, how about Seven Kingdoms: Ancient Adversaries?