If there is an alarm that sounding 24 hrs a day, yes, it can drain your battery.
I can't go by what somebody else said or didn't say. I can't go by what was or wasn't replaced. If you replace a component and the wiring circuit is faulty, it still won't work, even if the part is new. By the way, I'm not a fan of rebuilt parts. If you want to do some testing, I will try to help, but, you have to do the testing. Use a digital multimeter across battery posts, if you don't have one, get one. With the meter on, engine off, place leads across battery posts, The generic spec for a full charge is 12.6 volts, if battery is down, get it charged or we're just spinning our wheels. Usually the digital multimeter has a 10 amp setting, where you can check battery amp draw with everything off, On that setting you use the meter in series with one of your battery cables, engine off. A generic amp draw spec is around 50 ma, that is .050 not even a tenth of an amp. If the reading is very high, check for lights left on, interior--under the hood, where ever. Best time to check is in the dark. If that is ok, pull/replace fuses one at a time, when you pull the fuse on problem circuit, the drain returns to normal. Then you check everything on that fuse circuit to find the problem. If you want to check charging system, begin by checking for charging system trouble codes. Some of the national brand auto stores will check codes for free, if there are any. I don't know if they will check manufacturer specific codes? You can get an obd2 code reader. Your computer has control over charging system. Also, you can see fuses and fusible links. Check the basics before worrying about the pcm. Just my opinion.