How does the blocking FET Q1 exactly work in this case?
So the power controller is not being used at all when the wired supply
is detected?

When the controller detects a wired power supply it stops receiving wireless power and turns on the FET, so it is 'being used' only to keep the FET turned on.
The FET actually consists of two FETs wired 'back-to-back' to prevent current flowing through the body diode from the system back into the wired supply if it is a lower voltage or is itself a load (which is only permitted in USB On-The-Go mode).