I've had Google Maps in navigation mode for extended periods and if it's not moving it draws very little power so you could safely leave your phone in the car overnight from this perspective.
Google Maps doesn't need to be running on the phone. Even with no apps running you can use Google Maps on the infotainment screen. That's because you aren't actually running Google Maps, you are running the Android Auto version of Google Maps which is sort of like Google Maps Lite. Although it does use the same database and destination history as the regular Google Maps.
Thanks 2002. Have you or others had experience using a dedicated device for the Android Auto? I'd rather not inadvertently leave my (main) phone in my car and instead dedicate an extra phone I have on hand to the purpose. If the USB port could remain powered when the car is off then the phone would have power to remain booted, preventing the phone battery from draining to dead. Otherwise I'd expect to have to wait for the phone to boot up when the USB port gives it sufficient power. Most phones I've used won't automatically boot up into the OS when they receive power.
I'm starting to gather that your goal is to have a setup where your wife can run Google Maps on the infotainment screen as if it was built in. I think that's probably possible with your idea of using a second phone and keeping it always plugged in and turned on. The USB port is not powered when the car is not on but most phones go into sleep mode when inactive so you can test your phone to see how long it will hold a charge when inactive. What I can't predict is whether your phone will automatically come out of sleep mode when the car starts and Android Auto on the car attempts to access it. Worst case if it doesn't then she just needs to turn the phone on, nothing else, as I mentioned in my other reply you don't have to launch Google Maps on phone to get it to appear on the infotainment screen.
Also as long as Google Maps was the last thing on the infotainment screen when the car is shut off, then the next time you turn on the car it will automatically launch Google Maps on the infotainment screen. And that's true even if the phone is not plugged in when you start the car, as soon as you turn on the car it will attempt to load Google Maps but then just go to a black screen, but as soon as you plug the phone in then Google Maps will launch.
One thing to note however is that searching for destinations in Google Maps on the infotainment screen is not nearly as good as it is in regular Google Maps on your phone. So what I usually do is prior to plugging the phone in I go into Google Maps on my phone and search my destination, then press Start to get the route going, then when I plug in my phone Google Maps will automatically launch on the infotainment screen and the route will already be running. Maybe she will be okay with the search on the infotainment screen but I find it pretty frustrating compared to the phone version. Although I sometimes use the voice search when driving even though that is somewhat hit or miss.