Can whatever is draining my batterie cause weird and misfiring-sound idle? The idle is really annoying, and i think the alt might be causing the draining batterie. It drains when the car is off too.

I duno if the idle problem could be because of timing or the carb or the batterie draining prblem. i just need some help.
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so my first question is the first sentence i wrote-"Can whatever is draining my batterie cause weird and misfiring-sounding idle?" really low idle that just about stops the engine

 

its very slightly possible if the voltage is too low to produce a strong enough spark, although that is more prominant at high rpms. however, when my voltage regulator went bad in my car, it would be around 8-10 volts at idle but up to 18 at cruising speeds. you really should figure out whats draining the battery, then replace it once you figure it out. what have you done so far to find the draining issue? sometimes it just simple stuff that can cause it like water in the fuse panel or corrosion. usually if a battery goes dead more than twice it typicly doesnt last much longer, so it may just be that. my honda used to have that issue, i did a parasitic draw test and found only .03 amps being drawn with the car off but it would still die, so if it was going to be parked more than a week i would disconnect the power.