As far as I know we've never heard from the Awesomium developers; they don't mention which version of Chrome they're based on which makes me suspect they're not staying in sync with trunk.
That suspicion comes from the fact that the Chromium Embedded developer does participate in Chrome development -- to the extent that he keeps his project working -- and occasionally pops up on our mailing list discussing API changes that would benefit embedding.
PS: wonder whether the Awesomium people are doing the right thing by WebKit's LGPL license, hmm...