Don't know for sure but I don't think so. A better way would be to just re-wire the auxiliary outlet on the dash so it's always live. Very easily done. If you search the archives here You can find detailed directions on how to do it.
Yes, they are powered all the time. Most vehicles are powered by the same circuit that powers the cigarette lighter or 12 volt auxiliary power socket. That us why if your OBD won't power up, you usually have a burnt fuse going to the cigarette lighter.
The question would be, why do you want to start messing around with your obd port? There are too many other places to tap in.