killertomatoes, are you not already having trouble getting rid of heat from your CF lamps?
Aircon units only move heat from one place to another- and generate quite a bit of heat on their own. They do not make heat disappear. The heat must be put somewhere, normally into the airmass outside the building you are trying to cool.
Where were you planning to put the heat from both your CFs AND an aircon unit?
KT, your solution is to vent heat by moving your grow room air into another airspace, like an adjoining large room (which is itself well ventilated) or an attic. You might indeed need to cut a hole for a fan & ducting, hopefully so you can dump air into an airspace like an attic.
You just can't grow in a sealed closet, simple as that. A grow needs a really rather large amount of fresh air, much more than you can fit inside the building you live in- unless you live in a blimp hangar...
Your grow needs a ventilation system which is capable of moving about 3-5x the room volume worth of FRESH air in 3-5 mins max. It needs ducting which prevents re-drawing 'used' air back into the grow.
If I recall correctly, your room temps are running at 85F. TOO HOT! Your growth will be stretchy and buds will be fluffy and sparse. Must bring those temps down to about 80F max, more like 75-77 as an average.
Your problem is both where you are getting your fresh air from and where you are dumping your warm, moist air. Your temps are too high because you're re-drawing your warmed air into the grow.
Remember, fans move air- but they don't cool anything. People say they feel cooler when a fan is pointed at them because we warm-blooded people generate body heat and evaporate moisture from our skins. The evaporating water takes some heat with it, giving you the perception that you feel cooler.
If, in a sealed room, you point a fan at an object which is not generating heat (like a plant), it will remain at the temp of the air going through the fan. The fan's motor will actually be adding heat to the air in this sealed airspace.
Requirement #1 for any grow op is the ability to vent heat and draw in fresh, cool, CO2-rich air that cannot be cycled back through the grow.
Returning to the aircon question for a moment, yes- lots of grows use aircon, especially those which employ CO2 enrichment. However, even a very small aircon unit will use quite a lot of power- haven't seen any which draw much less than about 5 amps. When used for many hours per day to cool a grow op, aircon can get VERY expensive.