I had a nightmare where we bred some super plankton to capture CO2 and it quickly colonized and killed the entire ocean and we doomed the world. On the bright side, if this were possible, plankton would have already done it right?
So, unlikely.
On the plus side, since we descend from slimy things that survived the carnage, we have fairly good oxygen tolerance and completely removing all CO₂ might not even hurt all that much.