No because plant levels settle at a higher equilibrium. Plants may decompose but there are more plants growing at the same time, so it still ends up being more.

Higher CO2 levels are said to have led to a "global greening", in which crop yields have gone up a lot. This is especially true in Africa, so that reduces global hunger and increases wealth. The idea that more CO2 = less life is not as simple as it's made out to be. Climate doomers ignores this type of thing because they are convinced society can't handle complexity, so have to insist that CO2 is always bad even when it's not.

https://fee.org/articles/rejoice-the-earth-is-becoming-green...