the part where CC results in more CO2 output for all the energy it needs is usually the first thing mentioned.
If you're doing CC from air then yes but if you are using something like Exxon's CFZ technology then maybe not. CFZ is used on the production side to remove the "sour" stuff (like CO2) from natural gas before its burned.
BTW ExxonMobile built that CFZ plant in LaBarge, Wyoming and it's been operating for over a decade and its now being expanded.