Not for most of them. All the ones I've used will let you turn off/stop the navigation, but not pause it. The closest you can get is turning the volume off.
No, the X stops that navigation session entirely, and that's not what I'm looking for. Depending on where you are going, how many stops you have loaded, etc, you may not be able to easily start a new session. Breaking up the session also messes up any details about the overall trip, if anyone is trying to gather that.
Google Maps does have this function for Android Auto, so I'm not sure why the mobile Maps doesn't.
I've mapped a quick access button on my steering wheel to "toggle navigation mute/unmute". Best experience so far. Thanks to the engineer that decided to put that button there instead of a blank (when ordered without heated steering wheel).