My FO3 save works just fine on GOTY edition. Am at level 25 having completed all original side quests and have just left the enclave on the home stretch of the main quest. Have yet to do any of the DLC but have not had any noticeable clutching/instability in my game.
You can load the save on the GOTY edition from exactly where you were on the original disc. It may lag like a trooper for the first few minutes as it loads the add-ons.
You have to keep using the GOTY edition disc though, as the add-ons are notinstalled on the hard drive. I'm not sure what will happen if you use the normal Fallout 3 disc when you're in the Capital Wasteland, but if you're in an expansion at the time you'll end up back where you last saved it in the wasteland.