One such model is aptly named TRIFFID [1]
[0] https://en.m.wikipedia.org/wiki/Carbon_cycle
[1] https://www.nature.com/articles/35041539
Edit: non-paywall link to TRIFFID paper [3]
https://www.azimuthproject.org/azimuth/show/Carbon+dioxide+f...
> The details of CO2 fertilization matter a lot. It could make the difference between their original plan being roughly good enough… and being nowhere near good enough!
Check the page for more info on young vs old trees, nitrogen limits, etc.
There's also this page, which has an even more pessimistic take.
https://www.realclimate.org/index.php/archives/2004/11/co_2-...
Anyway after reading this I think I can answer my original questions a bit: Yes increased plant growth is a critical and part of climate change models. IPCC is predicting an increase of 6G tons of carbon consumed by plants by 2050 and without this we could not hit our carbon goals. Hopefully this research shows that our models are not overestimating here.