There's no danger of that. The most effective methods are fossil, so they basically remove what they are adding. Second most effective is artificial photosynthesis. But covering the entire planet with that would not make a big difference. Yes, it would be more efficient than native plants for removal of CO2, but not a lot more.
The only time you need to worry is if they propose a new unlimited power source like fusion and they harness it to remove ambient CO2. But we are a long way from that happening.
More CO2 = more plant growth. More plant growth = more oxygen released into the atmosphere.
Less CO2 = less plant growth. Less plant growth = less oxygen.
Unintended consequences: How much CO2 must be removed to initiate a catastrophic collapse of the plant life/oxygen system?