It is not possible, even though you can install PS on any drive, it still writes many files to the C drive. These are files used by other programs to talk to each other as well as some security files to moinitor where PS is..
Believe what you want is the new Cloud version of PS where you can access it from any computer. You do not "own" as copy, just rent it.
What Curt said. For technical reasons it's not possible.