Actually, I see no technical reason why this shouldn't work for JTAPI. JTAPI is completely independent of the user mechanisms... you can run JTAPI under a user account, or the system accoun t.. anything you like, and you could for instance have multiple services doing jtapi all running under different user accounts. I've accidentally launched one of my applications already running as a server (and thus different credentials than the logged in user) a bunch of times and it worked just fine (well... it did everything twice so fine is a bit saying too much.. but both application instances did work).
Of course, if you're writing something for end users, there are other considerations, but they are outside the scope of the question and they apply regardless of whether you're using JTAPI or developing something else entirely.