Yes any compressor should have a high limit switch that shuts it off at a set pressure.
Now if it is running without shutting off it could be a leak on the high side, poor compression, worn out, within the compressor, or a bad shut off switch.
I would suspect on of the first 2 since a bad limit switch would cause excess pressure and should pop off the safety valve on the reserve tank.
WBCCI 12156 AIR 3144 WACHUNG TAC NJ6
2004 Excursion 4x4
1991 34 ft. Excella +220,000 miles, new laminated flooring, new upholstery, new 3200 lbs axles