The US Naval Research Laboratory is developing a way to make jet fuel out of CO2 extracted from seawater. While this doesn't permanently remove CO2 from the sea, since burning fuel puts the carbon back into the air, it does avoid extraction of underground carbon.
"In close collaboration with the Office of Naval Research P38 Naval Reserve program, NRL has developed a game changing technology for extracting, simultaneously, CO2 and H2 from seawater," said Dr. Heather Willauer, NRL research chemist. "This is the first time technology of this nature has been demonstrated with the potential for transition, from the laboratory, to full-scale commercial implementation."
The predicted cost of jet fuel using these technologies is in the range of $3-$6 per gallon, and with sufficient funding and partnerships, this approach could be commercially viable within the next seven to ten years.
So far their demonstration setup can only fuel a model plane.
I posted a discussion about this on April 9th in the Origins group. The new fuel would not burn any greener than current ones. The questions are whether it would be safer and otherwise more ecologically friendly to produce and store. In that (as you said) producing it would not involve taking carbon from underground, making it would tend not to involve as many oil type spills and be more conducive to a natural appearance of the earth's surface. Moreover, the current cost of it is not very high and, over time, the cost would probably fall possibly leaving it very cost effective. However, this could result in an abundance of carbon based fuels so great that the practicality of using them would result in the development of more ecologically friendly energy forms being put on a back burner. In this way the new fuel could have a negative impact on the ecology. Per the second article of my Origins discussion on this:
....while seawater is an abundant and strategically useful resource, it will not be any greener or more carbon-neutral than modern fuels....