Is it possible to operate a control valve without a positioner
Yes, many control valves have I/P’s connected directly to single-acting actuators. A controller with PID will look at the process variable (PV) to increase or decrease the signal to I/P so that PV matches the setpoint.
It can still work with an I to P.
A Positioner is just an I to P (transducer) with position feedback, for better control.
An I to P will take in the 4-20mA signal and put out an equivalent air pressure, whether it is 3-15PSI or 6-30PSI, whichever you set it up for.