In theory, I think it's consistent with the first principle. The problem in that case is that we're taking up carbon that has been stored in the earth's crust for a long time, using it, burning it, and it's accumulating in the atmosphere. If we could find a way to capture the carbon, then in theory it would be consistent with that principle.
I think the question then becomes the most cost-effective way of coming into alignment with that principle. That's a different discussion, because you can evaluate different technologies and so on in that context. The important use of the principles is evaluating potential technologies for their potential to bring us into alignment.
I don't think there's any silver bullet, in the sense of one technology that's going to bring our whole energy system into alignment with the first principle, but certainly that would be among the options to consider. Without knowing more about it than we do right now, you could make a case for it being consistent with that principle.