Yes sure you have AGM but you do not have to upgrade to AGM.
The main advantages of AGM batteries is that they can deliver high burst of power on demand (Mandatory for Start/Stop technology, which once again, your car does not have!)
Charges about 5 times faster than a normal battery.
They do not spill in case of an accident
They can be mounted in any position.
AGM batteries cost twice as much on average compared to a standard battery. Your call. No real advantage in changing to a new AGM unless your car has Start/Stop technology. You have a start/stop button, which has nothing to do with the start/stop technology.
This is Start/Stop technology by BMW here:
http://www.bmw.com/com/en/insights/t..._function.html
Your battery drain may be due to a few different things too. You may end up putting a new battery in and still have a battery drain issue. Typically on e6x/e9x/e7x cars a faulty module could cause a drain. A faulty IBS sensor in the negative lead could cause a battery drain etc.