At least not today.
I’m working on various addons for Thunderbird, and one topic that came up a couple times was getting Weave to work with Thunderbird. So far, I have a patch against a recent pull of the weave repo, and a new addon called Weaver (yes, original) that implements some Thunderbird specific code, and a sync engine for the address book. Right now it will sync the two standard books, the “Personal Address Book” and the “Collected Addresses” book. There are still a few issues to iron out, primarily in the Weave preferences panel, and we’ll look at syncing a few more things that are easy and interesting. Have any data you want synced?
Also, this patch may well be useful for other xul apps that might want to take advantage of using a weave server to sync data.