This is totally wrong. Android apps don't work that way, if you close the app (pressing the back button) the app stays closed and is not consuming anything, as long as it's not meant to stay open in the background (and Top Eleven is not meant to be).
The game is not "constantly using anything to stay up-to-date". It only wakes up for a second to send you the notification if you have them activated. This is far away from consuming data or battery.