If you are able to install the OS onto the external HDD, you should be able to get the files you need. But only as a temporary solution, USB transfer speeds are too low to use as a HDD. Should work.
Program files though, probably not.. You see, you wouldn't be taking the neccesary files, like the registry files..
Depends on what you're getting, but if you plan on just taking a bunch of files from one programs folder and reinstalling windows, then replacing it... without any of the registry files it probably won't work.