yes open a support ticket,this sounds very odd.
I probably should. However, I think I've found the cause and a workaround. Maybe this can be useful knowledge to others too:
I wrote that there was noise with nothing connected, while what I ment to say was that there is noise even when the connected wireless receiver is turned off.
I got hold of some probing gear and started measuring. What I found is that the input-signal to the KPA is completely flatline regardless of whether the wireless receiver is on or off. Nothing registers on the oscilloscope in any audible frequency that could cause significant noise. There's nothing until the wireless transmitter is turned on. If anything, the output from the receiver is exceptionally clean.
Then I opened the boxes and started measuring inside. What I found is that there's a small difference in voltage between ground as delivered by the KPA's power-supply and that on the wireless receiver, with both boxes fed from the same power-strip. The difference remains the same when the wireless-receiver is off. It's well within what audio-interfaces are designed to cope with so nothing will break. What I believe happens is that the slight difference in voltage creates a ripple in the KPA's AD-converter just as it comes live, similar to when you plug in a guitar. This explains why the problem gets so much worse with delay or reverb as those effects keeps repeating the noise. Add some feedback in the simulation and you've got a high-pitched squeal. With no effects it is really just a loud tick.
I've been checking the powersupply on 3 more rack-mounted units from different manufacturers today and found small variations between the ground-signal of all boxes so this seems quite common.
My workaround is simply to boot the KPA to tuner-mode with the tuner set to mute the signal. I have been used to boot directly to browse-mode so far. A proper solution is non-trivial and would require modifications to both the KPA and the wireless receiver to enable interconnect of DC-ground between the boxes. That's no DIY-project.