Prompt gravity signal induced by the 2011 Tohoku-Oki earthquake - could this really be useful for warnings?
If you have a sufficient number of sensors, e.g., land-based or ocean-bottom seismometers, in the vicinity of where strong earthquakes typically happen, then it will take a few seconds for seismic waves to reach them, and a few hundred milliseconds for the electric signal to get to a place where a warning could be triggered.

On the other hand, the gravimeter would provide essentially instant warning. So you save a few seconds. At the same time, it takes many many seconds for earthquake waves to travel to the places where the warning would matter. In fact, the earthquake rupture itself may be many many seconds long. And it will take minutes for tsunamis to reach shore. 

In other words, what you gain in advance warning time is not actually very large, and it may not be worth the effort. I would also not be surprised if it takes tens of seconds or minutes to actually see the change in gravity in noisy gravity measurements, and/or to take the same amount of time to just process the data.