I haven't studied this in detail, but my understanding is that dark energy (whether from a cosmological constant or other sources) does not violate the "null energy condition" (roughly speaking, the condition that a light ray would never "see" a negative energy density). I don't recall exactly which energy conditions the Alcubierre drive violates, but my impression was generally "all of them". (His paper explicitly talks about violating the weak, dominant, and strong energy conditions, but doesn't mention null one way or the other.) There are quantum effects that seem to violate some of these, but my impression has been that the known examples do not violate them when averaged along an allowed trajectory in the spacetime, which the Alcubierre solution would.
That's getting near the boundaries of my technical knowledge of the subject, though, so I won't argue further. It would be awesome if this could work out, but as I've said elsewhere there are multiple Nobel-worthy steps between what we know today and actually creating any sort of warp bubble in the lab. If I were White, I'd be publishing my solutions to those first!
