Air operated piston pumps?

If the pressure ratio is 1:1, as for an air driven diaphragm pump where the air is on one side of the diaphragm and the pumped fluid on the other, the pump cannot produce pressure higher than that of the drive air. If your process could withstand the full air pressure you should be fine, though you must consider the effects of possible regulator failure or air compressor control failure.

But since your compressed air system probably has a RV [assuming it is properly sized, ie, can vent the total flow of the compressor, and also can vent air fast enough in case a fire is raising the tank pressure] you already have some protection there - UNLESS you have say 200 psi plant air but regulate it to 50 psi to the pump.

However, if you have something like a Haskell, where the pressure ratio is far higher than 1:1, then you would. However, if your process can withstand the pressure ratio times the max inlet air pressure, you should be OK, subject to the caveats above.

PS - I have had exceptionally good service from Wilden air driven diaphragm pumps, and uniformly rotten service from Sandpipers, and Sandpiper was utterly uninterested in helping me get their pumps running again quickly, even when I had just bought $20k worth of the damned things because they could supply them fastest.

Any positive displacement pump has the potential to over pressure the system into which it is pumping therefore they typically have a relief valve sized to match the capacity of the pump.

I would not be surprised to find that these pumps have an internal relief valve.

Also if the air supply has the potential to overpressure the drive end of the pump then it should also have a relief valve.