UPDATE: it appears that disabling sync from the UI doesn't actually disable it. See here for more info.

Do not, I repeat, do not utilize the offline sync feature in Thunderbird 3.0.x. It is horribly broken. It will suck down your bandwidth, consume your transfer limits and get your accounts terminated. It may also have sex with your dog, but since I don't own any dogs I am unable to confirm this.

This graph shows bandwidth utilization for a single instance of TB 3.0.3 syncing the last 30 days a 3.3GB mailbox (probably a few MB total to sync). I'd like to point out that this is day two of the sync:

You can see the dropoff about halfway through when I killed Thunderbird.

Best of all, it's a known bug and apparently no one cares since it's several months old and still not addressed.