No because we aren't reliant on a model of atmospheric CO2 concentration. We directly measure it.
Bear in mind, ESMs aren't trying to predict future CO2 levels. They're trying to predict future weather based on the effects of higher CO2, and vegetation is a part of that.
It's not very important outside of predicting the future of the climate accurately.
That's not the kind of thing I'd write "It's not very important outside of" before. This "mere" prediction and decision support is the reason we fund the sciences.