Somebody did some small-scale tests. It turns out that the specific gravity of CO2 in liquid state is higher than that of water. Even seawater. And the ocean is deep enough that if you pump it way down, the pressure will put the CO2 in liquid state.
So it's technically possible to sequester CO2 that way.
But there was a lake in Africa that used to have a lot of CO2 in it, and one day for whatever reason it was suddenly released and the village on the shore died.
Not something that would be good to have happen on the kind of scale it would take to affect climate.
And perhaps not healthy for the Badass and Delicious things on the bottom.