"Alternative" sources of GW

Probably not, because even the smaller quakes will cause the interferometers to loose their 'lock' and drop out of Science Mode. It's very difficult to isolate the instruments completely from the vibrations associated with any seismic activity: even a passing truck or train (near the interferometer) can be enough to temporarily disrupt the data collection. Of course this relates to a practical issue and doesn't address the fact that there should theoretically be gravity waves propagating from the acceleration of a chunk of mass during an earthquake.

I still don't know the physics well enough to do any calculations for what the result would be in terms of the theoretical change in length of the interferometer arms. Additionally, I don't know if the mass in question is sufficiently compact (or dense) enough to be treated in the equations as a concentration of mass in a single point, and if that's the case, then you would have to try detecting lots of smaller waves coming from the whole area of displaced mass instead of a single wave emanating from a point-source.

Interestingly, there are orbiting satellites (NASA's two GRACE satellites) that are used to detect density changes in the earth's crust from earthquakes, but only after extensive data analysis, which is far from detecting the changes in real-time, and not the same thing as detecting gravitational waves...

edit: You made a really good point about the waves arriving at the detectors before any of the seismic vibrations, so if it is indeed possible, then perhaps a hierarchical search of the data just prior to the instruments dropping lock might reveal something? :)