It would be like not having a filter at all... I had a exhaust blower die on me while I was at work one day, because of this no air was being pulled thru my carbon filter. When I came home I could smell my grow the second I opened my front door. And that was at the other end of the house, in a sealed tent, through 3 closed doors.
You will need to seal up that closet if you want that filter to be effective... If you're worried about the temps climbing too high with the door closed, the exhaust being pulled out through your carbon filter will help keep your temps down.