Just checked the numbers, for those interested.
A gas power plant produces around. 200-300kWh per tonne of CO2.
Capture costs 300-900kWh per tonne captured.
So this is basically non viable using fossil fuel as the power. If you aren't, then storage of that power is likely a lot better.
It's also worth noting that it is still CO2 gas. Long term containment of a gas is far harder than a liquid or solid.