I'm not sure about Ubuntu, as Linux is totally out of my ballpark. But I can say for Windows, well XP anyways [hopefully this is still applicable], that during boot up, Windows supposedly reinitializes the USB driver. The problem is that you are running off USB. What may happen is that you are half way between boot up and you suddenly get a blue screen, or something. You may still get on using safe-mode, and it doesn't really re-load all the drivers, but.. who really wants to run their PC on safe-mode?
I can speak for XP, is that you may need to repack the drivers. You basically go into you installation disk, extract the various drivers, and slightly modify them. Once you are done, you basically create a new installation, image of the disk, and re-burn. You should check online for Windows 7.
But truly, I'd go and check out some tutorials before posting. IMO, you'll learn a lot faster that way.
I kinda just finished writing this, and saw MadCat's comment. Yes, that is true. Just go online and type something like "WIndows 7 on External HD", or something. Good luck