most likely you will remove that application, bcoz neither it will save your battery and may it drain more battery than saving by closing app.
If your application remain in BG, it will just take some RAM not juice, and everytime single application try to kill appliction in BG with screen off will drain more juice.
there is also in built option for this if still you want it, go to setting - development option - limit background process, you can set your desired level.
Kindly don't PM me for routine Q. My Inbox getting full and missing important msg.