I have successfully transfered my Steam Doom 3 to Native Linux.
I have instructions, but they are vague since I am away from my Linux box.
1. Somewhere in the Steamapps folder (afaik) there is a receipt or .ini file or something left by the Doom 3 installer.
(Have a look, I shouldn't been too hard to locate it.)
2. Open it up in your text editor. You should find some references to some registry keys. These registry keys will contain the serial number for your steam version of Doom 3. The registry entries will be hashed. I doubt you'd be able to locate them without this file.
3. Find these registry entires using 'regedit' and copy the serial number down to a piece of paper (you cant copy and paste it into the game.)
4. Launch the game and put the serial number in.
5. Kick some ass
You can also move the saves across, but I also cant remember where to put them. (I opened up my doom3 folder for WINE and compared it to my native one. After that it because clear where they went)
Sorry for the vagueness. At least you know its possible though (for Quake 4 as well!)