I should have mentioned, this is a hard-wired system. There is no transmitter. I don't know if a wireless system would work, it would have to transmit through two 12" thick masonry walls over a distance of 60 feet.

Nonetheless, I had reached the same conclusion about dog-audible sound, but since the doorbell button is is probably sending a single pulse to trigger a relay to power the door chimes the delay seems unusual.

Thinking more about it, since the wire is also transmitting video as well as a signal to ring the chimes, I suppose it is complicated enough that strange things can happen.