Not really.
You're conflating the tax with spending the tax revenue. You don't need to spend any of the revenue on carbon sequestering projects. Just implementing a carbon tax that pushed the price of things like air travel up to the reflect the real cost would do a huge amount to reduce the amount people pollute.
If the price of a flight doubled then fewer people would fly.
Regarding air travel specifically, it's less (and decreasing) in terms of pollution relative to other forms of transportation. One of the sources: https://www.faa.gov/regulations_policies/policy_guidance/env...
Cars in sum produce more pollution than planes (at least in the US), and recent estimates say that the 15 largest ocean freighters produce as much pollution as all cars globally for a year.
So my feeling is that reducing global shipping - eliminating consumption of junk - and reorganizing cities to enable more walking/biking, would have a far greater benefit than focusing on air travel.