what type of fuel system do you have? return or returnless?
if you have a return style (97 and older) then the pump should be always on
if returnless then the pump uses regulated voltage to control pressure and if the sensor is stuck at max pressure reading then it may cause the pump to not run at all. Normally those kind of sensors fail are fail safe off. So it is possible.
If someone else on here with the same type of fuel system (pre 98, 98 and 99+) could test their working sensor's resistance at zero pressure and then are operating resistance you could see if its stuck at the max setting.