The Ubuntu Unity Messaging Menu integration extension has been updated, and now supports both 32-bit and 64-bit architectures!
But there’s a catch: in order to use this extension, you have to use Thunderbird 3.3 or higher. Instructions for getting Thunderbird 3.3 on Ubuntu Natty are here.
(Note: the instructions are for Ubuntu Maverick, but the steps are the same once you reach the Software Center)