ussnorway: the base answer is no because a portable drive is for storage and trying to run any software [not just games] off one in Windows is asking for corupt files
as a workaround you could temp move the patch to any internal drive in order to install it then move it back for storage again after... by default Gog patches assume the c driver because thats the only one you can say for sure is in everyones Windows system
imo hacking your reg without understanding what you are doing is just going to make things worse... if your system only has the c internal drive then a better fix is to upgrade the hardware to add another or bigger drive but i know thats not want to want to hear sorry
Every word of this is just nonsense.
1. You can game off external storage, just don't unplug it while you're using it.
2. Patches do not assume C, they check the registry for the location. My GOG games are all on various drives and they patch just fine.
3. Changing a few paths in regedit isn't "hacking the registry".