Yes it can, but it shouldn't. First make sure your battery is in good condition. First make sure your terminals aren't corroded. Then take it to a parts shop (AutoZone, O'Reilly's, Checkers, et al) they can test your battery. If the battery is good, ensure the alarm's wiring is in good condition. Frayed wires can short drain your battery quickly. Finally, if that's not the case, your alarm system might be malfunctioning.
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