Theoretically carbon capture can work, but just like you said, it takes additional energy to capture carbon, and that amount is more than what it takes to produce the needed electricity if you’re using a carbon based energy source.
That said, if you go for something like nuclear, than you do get a clean source of energy that can be used to capture existing carbon. But we’re already at the point where our energy infrastructure is inadequate for just electrifying what we currently have, and in a few years the Pickering plant is going to have to shut down due to being so old (though apparently the government is trying to delay it as there’s no plans for building a new plant of any sort to replace the Pickering plant).
So even in the best case scenario, it’ll be more than a decade before any sort of large scale carbon capture scheme can even be started, as that’s how long it’ll take to build enough new plants to cover existing demand, let alone accounting for future demand.