Will it grow?

For a 80x80 grow space, 600 watts of light is overkill, you would do well with a light between 250 watts (minimum) to 400 watts (max), I'm talking real consumed watts here. No amount of exhaust power will be able to give a temperature below your ambient temperature. What I would do is set the lights on at night and lights out during the day, that will help some; HPS give out a lot of heat (so does the ballast), switch to a good led that will help a lot too, actually a 250 watt led would be great (will help the electric bill too), something like quantum boards or led strips; finally you will need to get some AC unit, maybe not in the tent, but in the room where the tent (or grow space) is located in. If you do go with leds, stay away from burple (those purplish lights). If you have one, put the tent on a basement, they tend to be cooler than other parts of the house.

I have tiny tents (60x60x180) and had a 600w Sodium one summer, I can say it's possible, but I had a turbine extracting air, so much the tent deflated and generated lots of negative pressure. Also I had to use lots of AC to keep the room cool enough. And also had to inject CO2 to let the girls use lots of it and do not suffer the heat. Even then, I had burning on the tops, lots of unbearable heat, a huge power bill, and not so great results. Get a 600w equivallent LED, that will do night and day difference! Happy smokes!