I'm very sceptical to such claims, given the fact that plants and animals routinely deal with large and sudden changes already - changes much more sudden and much larger than the AGW movement assumes.
As an example, the air in an urban area may easily contain twice the co2 concentration of the air in the adjacent countryside. A breeze may replace within minutes said air with air
deficient in co2. Without any harm either to vegetations or animals either there or downwind.
Also, a typical living room may easily have triple the co2 concentration outdoors, yet the indoor plants suffer no harm when the air is periodically replaced.
Also, in order to increase yields, people sometimes elevate co2 concentration in their greenhouses to levels 10 times higher than the outdoor concentration. With plants suffering no ill effects from the fluctuations.
Also, humans (and presumably most other species) do just fine with co2 levels many times larger than the present one or anything likely to ever come about.
Sorry I'm too lazy to dig up specific documentation, this could be a start:
indoor co2 concentrations - Dogpile Web Search