The answer, in my case, is 0.23-0.25 seconds. This is pretty small, but still big enough that it could be an issue when say shooting live stuff through a microscope.
Here's the setup to take the measurement. The digital watch is for precision; the spinning disk at 1 rps is to cover cases where the digits are hard to read.


The same experiment with analog video and HDMI showed that those were faster, both around 0.12-0.13 seconds.
It's hard to wrap this up into an overall number for equipment delay. I know from other tests (HERE) that Live View introduces some additional and unpredictable delay between trigger and actually taking the picture. And if I wanted to shoot with flash there would be additional delay for dropping out of Live View as required to trigger the flash. Things add up...
--Rik