Carbon dioxide does indeed make plants grow faster in greenhouses, where they are not limited by nutrient availability.  (Even so, crops grown in high-CO2 environments are less nutritious than normal.)

However, outdoors, nutrient availability often governs.  Katharine Hayhoe, climatologist and lead scientist on three National Climate Assessments so far, says, "In a warmer environment with more carbon dioxide, plants do mature faster, but they build up less plant matter, so it takes more plants to get the same yield.  A large enough increase in temperature, or a change in drought risk can even eliminate those few benefits.  An experiment studying the relative effects of carbon dioxide on valuable crops, as compared to common weeds, shows that in a head to head match, the weeds win hands down.  Warmer conditions with higher carbon dioxide levels cause weeds to grow faster - up to three times faster than crops.  Not only that, but many weeds and pests are also limited by cold.  But as temperatures warm, these species are on the move too...  Weeds and invasives benefit more than most crops.  And high temperatures and changing rainfall and drought patterns are already wreaking havoc on food supplies around the world.  Since 1980, it's estimated, climate change has already cost us $5 billion a year on average in wheat and maize losses, much of that occurring in poor countries, where any change in food availability bites deep.  We are currently conducting an unprecedented experiment with our planet, and it's the only one we have.  Plants, animals, and entire ecosystems are made up of a multitude of intricate connections.  We may be altering those connections and affecting the species themselves in ways that we don't yet fully grasp.  But we do know one thing for sure:  the faster climate changes, the greater the risk for all of us."