My own comment on this article: "getting to, from and through airports is very time consuming"
I don't see how this would be any less time consuming. Security would be an equal nightmare - the only benefit would be that the citizens can utilize NYC/Londons existing transport infrastructure much like it's easier to get to the Chunnel departure station than it is to get to Gatwick.
Vacuum tubes could probably be built deeper down where the waves aren't strong. I actually think that earthquakes wouldn't necessarily be a problem at that level, since everything would have to be quite flexible anyway. In order to elevate security, I could imagine making tube sectors detachable and having safety shutters. This way, if one sector is breached it could be sealed and detached such that it floats to sea level. The train could even be inside if you can control the pressure differences well enough to not kill everyone inside (something that is well understood for jet planes).
I'd say let's wait and see what nanotechnology gives us :).
You have your answer right there.