Let's see now.
lens opens completely, fires transmitter, transmitter sends signal to receiver, which relays it to the flash. Eventually the shutter closes.
Electrons travel at/near the speed of light so the slowest part of the chain is the shutter. Then comes radio waves, then flash. Blink!

Wonder how long it takes for the flash to respond to the closing of the switch?

All you need to do to test is look through the shutter at it's highest speed and trip the flash. Light = it's working at the highest speed.