PhillipEarl: I have absolutely no problem at all running them from a USB stick. I usually run windowed mode, but have confirmed that they run full screen, patches and all. I haven't checked the registry, but the only thing I've found that it leaves behind are copies of the .ini file in the Appdata/roaming folder.
EDIT - I should note that I have not installed Fallout Tactics as of yet, so can't tell you how compatible/portable it is.
vodkaassassin: I really do not plan on playing Tactics, not a big fan of the RTS style they went with that one. Have you got Fallout 1 installed with FIXT on a USB and it still work?
Sigh. I thought I had, but now that I look in my game folder I have the TeamX, Hi res and Fallup Mods. Fallout 2 has Sfall and the F2 Restoration project. No Fixt. The mods sticky was sort of confusing for me at the time, although I'm not sure why. Going back and re-reading I would probably have just installed FIXT.
However, unless FIXT is providing you with an new exe I don't see that it would make a difference. Try this - install Fallout to a computer or another stick, copy the folder to your main usb stick and uninstall the original. Heck, make two copies of the folder. Then uninstall the original and install whatever patches you want to try out on your first copy. If FIXT doesn't work portably, you can always go back and install the ones I mentioned above to your second copy and use that one. Might defeat the purpose if you were wanting to try out FIXT, but if you're just wanting to play Fallout 1 and 2 on a stick then I'm pretty sure (so far) that the patches I installed work.
I'll know for sure in about a year when my rather glacially-paced playthroughs are finished. :)