simple electronics...YES eventually (and maybe not in so long....)

I have an after market system fitted to my 940 turbo (ok its a very heavy duty system including radar cloaking of the vehicle, two point imobalisation, dual flashers installed in the front doors -blue blinking leds next to the door buttons ...;-0 - and a bleeper that activates (quietly) anytime anyone comes within about 2 feet of the windows) It pulls abotu 200Ma (about twice what a standard aftermarket pulls accrding to my digital meter...)

now if you have a 60ah battery thats 60 000 mah...
so

to totally flatten the battery....

60000/200 = 300 hours or 12 days...but of course we dont need to totally flatten the battery to stop a start.say 1/2 discharged may well do that on a slow discharge....so 6 days....

Now assume your factory system is MEGA efficient and pulls 1/4 of mine thats still only 4 times as much or 24 days....IF your battery is FULLY charged and in good condition....

so the answer is yes...eventually.... the easy way to tell is to connect a amp meter between the battery and the live feed and then lock the car and see what its pulling..then its down to maths...(DO NOT START THE CAR WITH THE METER IN PLACE AND ENSURE ITS CAPABLE OF MEASURINGAT LEAST 10 AMPS - but also of displaying Ma!)