We have a bug open to add Twitter crossposting (and Facebook, and Wordpress, and Movable Type, and and etc) -- the issue with each of them is that you have to a) implement the remote site's posting protocol and b) work out how it would map to DW. (For instance with Twitter, figuring out how you would handle the metadata like current mood/music, figuring out what to do if the post is over 140 characters, etc.) So yes, it's possible! It would go into cgi-bin/DW/External/XPostProtocol
and get hooked in somewhere (I'm not sure where). (And if you get it working, give us the patch. *G*)
I don't know TT or how to work the beta features, so I'll pass on that!