As a continuous observation network looking out for submarines?

If so, maybe, but that would entail an enormous amount of sonar going into the water that could have significant ecosystem effects. But I don't know well enough the effects of sonar on marine life. Something that substantial would certainly bring in the cost verse benefit analysis.

I think its a better idea to think about Space/low earth orbit satellite networks in terms of continuous observation of frontiers first. More cost effective and a wider range of uses.

I'm not sure what other purpose but defence you could put continuous monitoring of the seabed to use in. I suppose there'd be marginal benefits from seafloor disruptions through tectonic plate movements.