In general terms yes. All the conditions are there that could lead to
use of PID. There would be special conditions applied to the magentron
control, nothing insurmountable.
I want to say it was Panasonic that has been doing similar for years. I know they have also gone with Inverter Technology on their microwave oven product line. This is another real good write up on the newer technology, note how the power levels used are changed. While not PID it is pretty cool.
There is a fundamental incongruity in the concept. The magnetrons used in microwave ovens only operate over a small power range and analog control is not generally done. And most PID controllers tend to be analog, I think.
The challenge of modulating power to a magnetron in a microwave oven is that the tube heater is powered by the same transformer, and so power cycling the transformer can cause problems. At that point the control is the same as what it comes with.