Far as I know they all unload when the motor stops I wouldn't bet on starting against high head pressure.
I think the answer is closer to what clare wrote. In looking around, the motors I saw on compressors were capacitor start, capacitor run. Those motors, in general, have relatively high starting torque and relatively low starting current for that torque. I have seen no reason to believe "special compressor motors" are anything but standard cap start, cap run motors.
The problem I have is Jon's 3HP SPL motor. It is a scam rating. Just like the scam ratings that resulted in the class action lawsuit, which the manufacturers settled. If Jon knew it was not a real number then why post it? (And then there was Jon's 2.3HP miscalculated value.)
A scam "peak" 3HP motor has a peak (near stall) torque that is equal to the normal running torque of a 3HP motor. It is not the starting torque of a 3HP motor.
For many of its smaller compressors, Grainger gives both the scam "peak" HP (competitive with Jon's scam rating) and a real HP.
I haven't seen any reason to believe that the "real" HP is not the appropriate rating. Because there are plenty of scam ratings, you can't compare compressors based on HP rating (as many people here have said). Even with real HP ratings you need to compare the air you need with what a compressor provides (also as many people here have said).
============= This is similar to joule ratings on surge suppressors. In that case there is not a defined way to measure the joule rating. So some manufacturers use deceptive ratings. As a result, some major manufacturers no longer give a joule rating.