If a typical car battery is about 45 amp hours, and I'm pulling 20mA or so, does that mean it would have to run for 1125 hours (almost 47 days) to half-discharge the battery?
Yup. Unless something shorts out, you won't drain the car battery with the Arduino.
I guess the math is correct but I'm surprised. 20ma seems like no load at all but 47 days is not an outlandish period for a car to sit idle and having half my battery drained by my door lock key pad seems a bit alarming. Maybe it's a Canadian winter thing but I'd be worried!