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Actual test I just did: my Behringer mixer (fully analog) introduces 3.3µs of delay from CH5 to TAPE OUT. That's 900 meters at the speed of light, and I only had about 0.5m of additional wiring, so it's not a speed of light issue but rather analog processing delay.
So no, analog hardware does not have zero latency. Small, yes, but not zero. Digital logic is certainly fast enough to do quite a bit of processing in 3.3µs these days - definitely good enough to emulate the equivalent of the three-band EQ in the Behringer in the same time.
