Let's say your original source could be heard by the audience. The audio can travel from source, to mic, be digitized, transmitted over IP, arrive at console, be digitally mixed, then transmitted over IP to speaker, then broadcast at an unknown distance from the source. How much latency occurred there?

The trick is to get the original source wave to roughly line up with the time the amplified wave leaves the PA speaker, otherwise weird echos are heard by the audience at best, and awful band-specific noise cancellation happens at worse.