Mine does have an alarm, but I've left it powered on at night when I got home from work a few times and the batt was dead in the morning (usually winter only). If you can't hear the alarm from inside the house, it's not much good.
Low voltage shutdown would be nice. It's a crappy feeling walking out to my van in the morning when I'm running behinde and hear a slight beeping coming from inside my van.
Just checked and it looks like the one from costco has:
Overload and over-temperature shutdown
Over?voltage protection (15 V DC)
Low voltage alarm (11 V DC)
Low voltage cut-out (10.5 V DC)