No, the phone does not silence itself when it detects motion (which could really only be done via cell handovers or GPS - an accelerometer detects acceleration, but not steady motion).
I can only guess as to why you had no audio output. The audio being routed through another device (bluetooth or wired) that was not itself outputting does seem a possible explanation. Otherwise all I can think of is the volume being turned off on the phone, or navigation mode not being engaged (though that last would be very obvious to you, so seems unlikely).
If you were using Maps, I just tested by telling mine to navigate me to work (while sitting in my living room) and it started speaking almost immediately, didn't wait for me to start moving.
