Part of the problem with protection systems is that if you are dealing with displacement probes you often can't access them without a major outage.
Being on the sales/service side I see a lot of customers who will regularly induce signals to simulate a trip situation, some do it as a regular PM, I have one that does it as a part of startup after any major maintenance. I've seen it done with both a signal generator and connecting a spare probe into the driver and using a wobulator or shaker.
If it is only being used for shutdown, I recommend a regular inspection, ensure the right lights are on and there are no obvious issues; bad sensors etc. If the system is being used for analysis, those bad sensors are easily identified.
Many systems have internal calibration sources that will do a self test, so the big question comes down to sensors. Understand that you don't actually calibrate accelerometers, you can't adjust them, you just validate the calibration. So pulling all the sensors out and sending them in for calibration is a waste of money. I recommend putting a portable shaker on the sensors to validate the entire chain from sensor to rack, I see a lot more cable problems than sensors.
If you are doing an outage where a turbine covers are coming off, definitely pull the probes and do calibration curves on them.
All that being said, in many cases if the system is just used for shutdown it belongs to the instrument technicians, they might not know vibration, but they understand inducing voltage signals to validate equipment.