Exhaust System Question

I am using a 4x4x6 tent with a 6 inch VenTech blower fan and a 600 watt light with an air cooled hood. Curious if it's a bad idea to hook-up the carbon scrubber air filter directly to the intake of the air cooled hood or do i need to be drawing fresh air for that?

My idea: (Air Filter)>>>>>(Hood)>>>>>>(Blower Fan)>>>>(Exit)

What i believe most people do: (Air Filter)>>>(Fan)>>>(Exit) &
(Intake tube exiting the tent)>>>(Light)>>>(Blower Fan)>>>(Exit)

Run filter-fan-light-exit. That's what I'm running with a 6 inch booster fan on the intake. Even have the same fan as you with a adjuster plugged in. Working awesome. Oh just make sure you take the pamphlet out of the van tech or you'll find it in the fan sounding like a bearings going out. wanna know how I know? Lol also you won't have to worry about the fan suckling stench in from leaks in your hood and such.