Yeah probably. I suggest if you make the coop and dm do it based off of Skulltags multiplayer. Heres their link
http://skulltag.com/Youll need a copy of any doom or heretic/hexen (im not sure about Strife) to play it, and they cant be the Steam versions
Also if anyone finds a Doom map editor thatll run on 32 bit Vista, send it my way. Itll be a lot easier to use that than try to run around in the game copying it
Edit: Never mind, i got Doom Builder Working