We have a SQT18MS with live tooling, it requires air to connect the live tool drive in the turret, as well as blow off the tool eye. It will throw a low air code with no air.
Our QT30 has no live tool and only uses the air for the tool eye and will not fault if there is no air.
If you are serious about bypassing the system you will have to trace where the air goes into the machine, find the pressure switch and by pass it there. If it's a two wire switch and air pressure closes the circuit you will have to solder or jump the two wires together, if it's an open circuit switch just unplug it.
I wouldn't recommend the bypass because if your running a part and loose air, it will still think it has air, activate the live tool, turn the motor on without the tool holder being locked in, and it will keep going with a stationary tool and crash.