I don't get why everyone finds this great since it takes a very long time for carbon in the atmosphere to get trapped in seawater.
CO2 in atmosphere -> CO2 in water -> Ocean acidification[1] -> Change in ocean ecosystem
The oceans absorb OC2 from the atmosphere, which you could argue is good, but it is not without consequences. Putting CO2 in the water moves the problem from having it in the atmosphere elsewhere, but it's still a problem. In some ways then, this can be seen as a good thing, because it is undoing the effects that increased CO2 in the atmosphere has on the oceans. Obviously though, I doubt that its effects would be at all noticeable.
The wiki article already linked has a chapter called 'Possible Impact'.
The ocean presently has a lot of extra carbon, which it absorbed from the atmosphere. So this is an indirect way of taking carbon out of the atmosphere and then putting it back...a closed loop. If we did this for all our hydrocarbon fuel we'd be carbon-neutral.
1. Take carbon out of the ground, where it is not active in any carbon system. Put it in the air, and ultimately the ocean. This releases more carbon into the whole system, and causes problems we all know about. It eventually goes to the water as the parent mentioned, with the acidification problem (s)he brought up. Adding ever more carbon to the system only adds to the total carbon load.
2. Take carbon out of the water, reduce acidification, albeit by transferring it to the air. This doesn't actually put new carbon in the system tho, so it has benefit.
However, the carbon put in the air with #2 is the same as traditional jet fuels from sources in the ground, so those effects cancel out as a consideration in our choice range.
Sure in a perfect world, we would find a way to start actively reducing the amount of carbon in circulation, however, to get there we have to find ways to stop adding new carbon to the system. This helps with that.
[1] I know there are lots of options we could consider, but I highly doubt any option that effectively translates to "have the military be less effective" will fly politically, so I am assuming that short-term achievable options have to have no negative effect from the military POV at minimum.