Is it considered feasible to genetically improve plants for better Carbon dioxide breakdown?
I'm not sure from your question if you're clear on the relationship between carbon fixation and 'energy', so just to be clear: carbon fixation in photosynthesis is the process of capturing CO2 and using it to store light energy in the form of carbohydrates. More CO2 capture = more harvestable 'energy'. Improving the efficiency of photosynthesis therefore captures more CO2 and generates more harvestable energy in the form of carbohydrates (edible or not).

There are three carbon fixation pathways in plants: C3, C4 and Crassulacean acid metabolism (CAM). The relative efficiency of the different pathways depends on the environment; for example, C4 plants are able to more efficiently fix carbon in drought, high temperatures, and limitations of nitrogen or CO2.

Because of this, scientists are indeed interested in engineering crop plants to use alternative carbon fixation pathways. One such project is the C4 Rice Project: http://c4rice.irri.org/.