No, *animals* respire CO2--trees fix carbon in their tissues and so sequester carbon from the atmosphere. The process of photosynthesis involves splitting the CO2 and 'scavenging' the carbon; the oxygen is released to the atmosphere.
Actually, a significant fraction of human-emitted CO2 ends up in biomass on land--a lot is also absorbed by the oceans. Only about half remains in the atmosphere. It's not clear how long that will continue to be true, though--as seawater warms, its capacity to absorb CO2 declines.
And of course, when plants die, they decay and release either CO2 or (worse in the short term) methane, CH4. So as warming continues, plant mortality will likely increase, and that will release yet more greenhouse gases.
On the other hand, CO2 does encourage plant growth--though other conditions (like sufficient nitrogen, phosphorus and water) have to be met for this to be a significant help. But that effect may help to offset some of the carbon release I mentioned in the previous paragraph.
Hope you don't mind me going so far beyond your question in responding, but I think this stuff is very interesting--and of great practical importance in the long run.