You can find the PJ Link protocol specification at
https://pjlink.jbmia.or.jp/english/data_cl2/PJLink_5-1.pdf On page 25 you can find the AV Mute Status query message, which will give feed back on the stat of the shutter.
Unfortunately AFAIK there is no way for QLab to be able to read the response from the projector (no ability to add a handler for message etc).
So you would need some external software to process the response and then send a signal to QLab (like OSC to run a cue).
But basically, providing the control position can see the stage, I would advise the operator to look at the projection screen and check that the projector is on and the shutter is open. This is much more reliable! You should always run a video rig check before each show.
Note also you should always turn on your projector before starting QLab, so the utility of a feedback function for power on is dubious.