What you need is an app that will kick off when you attach the USB drive. I've got an old Maxtor One-touch drive here at work; it has a button that you push to run the preconfigured backup software.
I personally would just set up backup software to backup that USB device, and then run it when I plug in the USB drive. You could create an autorun.inf on the USB drive that runs this for you, but then you'd have to enable autorun. I keep autorun disabled for security purposes.
One trivial approach is to use uSoft's briefcases. Create a briefcase on the external drive, copy the folder into the briefcase. When you attach the drive next, right-click on the briefcase and choose synchronize all. It will even copy files that you updated on the USB drive back to the hard drive.
So there are some options. I don't know of any way to do exactly what you described, to have plugging in the USB drive trigger a sync.