No, you'd need to restart the level
Its an issue with Project Cartographer itself rather than the game. I'd recommend you to get the GFWL client if your going to play campaign. That way, you can remove the Xlive.dll found within halo 2's install dir (if your going to play campaign) and put it back there if your going to play MP (You'll also get access to campaign achievements if you login with an Xbox Live profile)