If the gauge is reading inaccurately however, could I just checked the air pressure in the pressure tank to get an accurate water pressure reading? As the water pressure builds against the air pressure in the tank, the air pressure should also rise, correct?
Yes, that would tell you the pressure in the system provided your air gauge is accurate.
You should know that a pump running continuously while no water is flowing in the system will burn up in a very short period of time. First the impellers which are almost always plastic melt. Then as the heat continues to build, the motor finally dies. It would only take one or two melted impellers to drop your pressure to 20 psi or so.