Maybe I’m crazy but I think the OP is asking whether to create a closed/circular system, that cleans the air and pumps the same air back into the tent.
OP: You definitely want to scrub the air and vent it outside the tent. You do NOT want to return that “scrubbed” air directly back into the tent. If you do that you’ll, eventually, deplete most of the CO2 in the air, which is what the plants need. The single exception to this would be if you’re running a sealed tent with a constant CO2 source. You need a way to get fresh air into that tent. I believe that many closet growers, because of the doubly enclosed space, will install an intake fan that pulls air from a room with a larger volume or from the outside. If that’s not possible, it’s not a deal breaker; but you sure don’t want to to recirculate the air back into the tent. The advice regarding pulling or pushing the air through the filter is accurate.
I’m setting up a bigger tent and I’m pulling the air through the filter and then venting it (through a duct) to the outer room. The outer room has some Ona in it. You might look at using some Ona products to help with your situation also. Then, I’m attaching an additional intake fan (that’s 1/2 the size of the one I’m using to clean and vent air) to an air duct I have access to and it will blow fresh air into the tent via a lower duct. So, fresh air is pumped into the bottom of the tent and pulled up (through the canopy) to the carbon filter at the top, “scrubbed” and vented outside the tent.
Hope this helps