Does the motorola droid allow you to swap batteries without turning it off?

Doubt it. This “feature” is no different than any other phone (except iPhone).

If you plug it into the power then swap the battery… I just tried it on my droid.

The battery gives it it’s power, there is no secondary power-source that I am aware of. If you remove it… it loses power.

Does your car allow you to swap batteries without turning it off?

what @mowens said. i just tried it too.

actually you can… you pull the positive cable off first it will run on the alternator. very quickly remove the negative cable, the car will bog down but it will have a floating ground and you hook it up right away. so yes you can… way to make a smart ass comment when you know nothing about what youre talking about