You *can* do things that way, but there's no reason to, really, unless you're going to do some co2 stuff. If you're primarily growing for yourself, forget co2, and just use one big fan to pull the air into the box via passive intakes, over your light, down some ducting, and then push that (stinky) air through a carbon filter and expel it out of the box. This is the simplest and most cost-effective way to provide adequate ventilation while keeping odors to a minimum.

Here's a pic of my box, which is probably clearer than my typing. The passive intakes (Doran 8"x8" lightproof darkroom louvres) are at the bottom (I needed two of them to provide enough airflow). The air enters there. Inside the cabinet I have some oscillating fans to mix the air up. The air is then sucked into the cooltube and over the light, then blown out the top through a carbon filter (which you can't see, as it's hidden behind books and crap on top of the cabinet).