Yes, but barely, and you have to keep the ignition on. We’ve been considering some wiring changes on the Suburban to power just the OnStar system and setting up a WiFi repeater for the trailer, but we’re waiting for the bumper to bumper warranty to expire. Also thinking about locating the WiFi antenna in the OnStar system and making it “movable” and remote to position it inside the trailer. Haven’t gone exploring yet... Then you get into electrical usage on the TV, how to charge it, mixed battery types, blah blah blah.
We also want to do this to make it possible to shut off OnStar while rolling, as it sometimes needs to be reset when crossing the Canadian border (OnStar WiFi is a North American plan, and works great in Canada). We don’t want to stop, turn the motor off, get out for 10-15 minutes, then restart to allow the OnStar unit to reconnect in Canada (which is what their tech support people tell us to do). We travel through Canada monthly, and this saves us the expense of North American phone plans. We go airplane mode with WiFi only. Works great.