No it does not.
I have 3ea 430W HPS(sometimes +2 ea. 430w LEDS) , my detached room size is about 10 x 10 x 8; with 6" walls insulated. I don't heat this room anytime during the winter(LOW TEMP 17F) , other than the lights. My out-side temp right now is 43F, inside temp is 83.3F; With 10" and powered 6" intake into room, and 10" exhaust powered by >750CFM on a thermostat [set-point 78/5diff.] . my lights are 24/7, With an oscillating mixing fan. I know this is not like your set up but I wanted to give you an idea why I said NO.
You need more CFM's.
With only two small fans (cfm wise) I seriously doubt you are moving 400+CFM because of wind resistance around your lights & through ducts & filters in your configuration. (My set up will pull the door closed.)
Why are you heating the last 600w lamp with 2 other 600w lamps so that it has to dissipate heat into HOT air???? Have you considered cooling lights in parallel instead of your series heating/cooling?
The 8" fan might be adequate for one leg of your set up, I could be wrong, but it just might be that the two small fans are limiting the INPUT to big fan. Try an experiment: Check volume of output from 8" "{ with & with-out 6"s Running} !
I wouldn't add AC until I made the CFM adequate, unless you have an extra $2-3/day.
Double the pipe diameter and you quadruple the Volume. Pi(3.14159) x radius x radius = area ........ 4"=12.5sq.in.
8"=50sq.in ................