Dead FOB Battery?

The other day I was traveling, about 400 miles from home. Stopping to get coffee, I left my Fob on the passenger seat and locked the door using the switch on the door. I did not realize it at the time, but the door locked with the fob inside. Normally one can not lock the door if the sensor notices the fob inside the car. Of course, when i returned to the car, the doors would not open and i was locked out. After AAA opened my car door, i was not able to start the car, so i put the fob in it's receiver and the car started.

I then realized that for the past week after turning the car off and opening the door, i would here one beep. Not knowing what that beep was for, i ignored it which of course was a stupid thing to do. Since the car was not recognizing the fob, i replaced the battery in the fob when i got home and wala, the fob began working normally. So, I am assuming the beep i heard was a low fob battery warning. Is my assumption right?