Gravity detectors work from moving aircraft (it's a common method of deployment), so motion's no problem and can be made incredibly sensitive—sensitive enough to suit the job in hand (place one on a table and then on a book on the table and you'll easily read the difference in gravity). Moreover, seamounts are incredibly large objects and would have huge signatures and thus easy to detect.
I'd suggest the real issue around this matter is that it'll be classified.
We'd have difficulty in fitting LIGO in a sub methinks and seamounts are static and thus no G waves. You're right though, I should have been more specific, perhaps a more understandable description would be a mass detector or sensor.
I reckon the reason we don't hear much about this subject and the reason it's likely classified is that's its primary purpose would be the detection of other subs, detecting seamounts a secondary benefit.