it si the key in ign arm that trips the buzzer , I hate the buzzer , basically it will have no effect on the lock operation
BTW the lock always goes in & out Without the key in the lock
new lock assemblys are easy to get fro about $20 from BLUE Streak / Standard , the outer trim ring is often loose & swivels due to a weak / broken tab that keeps it in place , the lock can be keyed to your door key by a locksmith or I will be happy to buy 1 here , match you key code & send them out if needed