You can run programs from an external HDD, just donot expect them to remember wheter they're registered or not. They cannot create registy entries, it seems, so they will not hold that sort of information. You can save files you are working on. I donot know if you can set personal preferences, shoul you want to.
I have a photo editing program I use during my study, it seems like it's forever in Trial mode due to it being on my external HDD..