exhaust fan is greater than the carbon filter and the air intake, problem?

So i have a 9x9x13 grow room, 1200BTU for intake, which is equal to 400-450CFM based on what i found on a google search, and a carbon filter unit called blueair http://air-purifiers.findthebest.com/l/12/Blueair-203 - it has a 141CFM fan, and an exhaust fan of 550CFM i got it for a 600watts air-cooled hood to exhaust air/heat outside the room, I've read some threads but it seems everyone has a different opinion...
So my question is will the the carbon filter do its job with having that exhaust fan of 550CFM and intake of only 1200BTU (400-450CFM) ?

All I can say is trial and error my friend........good luck.

yes it will. your window unit recirculates the air in the room to cool it. it doesn't bring in fresh air and cool it on its way in.