Yes, test the circuit like wbwood suggested. You can use a needle to pierce the wires so you won't have to cut them then splice them back just to test. I did the same installation for the same reason. In my 5th wheel there were three wires - a ground, a switched lead and one that was hot all the time near the old unpowered vent. Don't know why it was there, but I didn't question it - just used it to power the Fantastic Fan. Negative will probably be white, hot will be black or brown. The Fan doesn't pull much power.
No more smoke alarms while cooking breakfast...