yah, unless you have deep cycle batteries your factory battery will be weaker next time you charge it. ive toyed with batteries in the past and in general, once your battery is drained it will only recharge about 85% or less at best. your CCA drops too. keep doing that a few times and your battery will no longer start the car effectively and burdens the alternator.
i would remove the battery given your choices and recommend you put a battery tender on it while in your house.
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