Depends how long, I think after a couple hours it may, but I can't confirm.
About 30 minutes or so before I think about going to the car I check on the app again just to be sure, but I need to activate climate anyways usually. I except when I'm leaving home, then I just get near the car and open the app and it takes 3 seconds max to open up
But when I'm out and about, it is long enough in the background that I don't have to touch the app again.
Try the widget, I noticed it checks on the mileage of the car and updates every few hours. I wonder if that keeps the app alive?