I missed this post because it was wrongly attributed to stevo.
It is a worthwhile question and worth a considered answer.
Growth rates in plants are going to depend on myriad factors but there will always be one factor that is in such short supply that it's availability limits growth. Sometimes that limiting facto will be CO2 and there would certainly be some places where plants growth rates have increased to take advantage of more CO2. However in most places some other factor runs short so extra CO2 doesn't help. There is synergy between water loss and CO2 intake so more CO2 does help plant growth in dry places. Additional growth doesn't help too much overall because atmospheric CO2 levels are rising year on year.
If warming temperatures cause an expansion of boreal forests into tundra one might reasonably assume it would create another carbon sink but warmer temperatures are causing tundra to lose carbon as well.
