Yes. It could be the cause. Not so much the light itself, but what it represents - ie an alarm system constantly monitoring the car,
It can be the 'straw that breaks the camels back' if the battery is not getting much charge due to short infrequent journeys. Certainly over a period of a few days.
If the drain is major -eg from well charged to completely flat overnight then maybe there is another cause, such as a faulty battery, or lights left on. By lights I also mean interior lights, or the boot light not going off as it should .
I once had a main dealer fitted alarm system on a car. It frequently flattened the battery due to parasitic loss. I discovered this was the cause when I unplugged an optional extra 'shock sensor' module ,which although hidden away, had a flashing led. Problem solved.
I dont suggest you disable the alarm. The occasional trickle charge, or long journey ,may sort things.