The issue is addressed explicitly in Alcubierre's paper where he mentions (at least twice) that there are no closed causal loops in his metric. So there's no violation of causality, and the standard intuitions from special relativity don't apply. Pretty remarkable! The lack of closed causal loops apparently follows immediately from standard results about the sort of metric construction he uses. There's no need to invoke Geroch.
I'm not surprised that Alcubierre addressed this point, though I'm glad to hear that for certain. (I've done little more than glance at his original paper... I never have enough time for all the cool stuff.) But my understanding is that his metric is "eternal", in the sense that the warp bubble exists into the infinite past and future. That's obviously not practical for any actual application of the idea (as you'd need in a "warp drive" as discussed in this original article).
Instead, people want to find a way of creating a similar warp bubble where one did not exist before (presumably analogous to the way that stellar collapse creates a black hole that eventually approaches the Schwarzschild solution). So my question is, if someone does eventually find a GR solution that "creates" a warp bubble, would it be possible to patch multiple such solutions together in a way that allowed closed causal curves? (I'm imagining sending a warp "pulse" from Earth to a distant star, then having the recipient boost into a different rest frame, and then send a new warp "pulse" back to Earth, for instance.)
The answer may still be a clear "no", mind you. But it's not obvious to me what arguments you'd use to show that (particularly since we don't know what form a "warp bubble creation" metric would take, assuming it's possible at all).
