Yes, multiple outlets are permitted on the same circuit. When the proper overcurrent device (circuit breaker is one example) is used, it will operate if the circuit is overloaded. I recommend that air compressors be on separate circuits since they often operate coincident with other loads.

You my get away with it depending on the motor starting loads.

It is NOT a violation, but a separate article for motors (Article 430) allows their breaker size to be divorced from the conductor size to allow starting.

The wring needs to be 120% of the motors full load running current, from a HP table in the NEC (NOT the motor nameplate).
A typical inverse time breaker is then allowed to be larger than the wire size fr general purpose circuits by a couple hundred percent.

A motor that has a full load current of 15 amps would need wires rated at 18 amps, so #12.
The breaker might need to be 30 amps (or more) to allow for reliable motor starting.

The breaker is there only to protect against shorts in the wiring.

The motor has its own internal thermal protection that prevents it from overloading the wire.

The AHJ might have an issue with the breaker not matching ALL the motors that could use the circuit.

I mark the switch plates "MOTOR ONLY" just out of habit.
Maybe it will keep the next owner from just jamming any ole' 240 V load in there.