Blowing hot air around inside of the tent will not cool the tent down.
You need to exhaust the hot air from the tent somewhere other than in the same room the tent is in. No amount of blowing air in will alleviate the excess heat in the room.
Yes and no...
The movement of air from a fan wont remove the heat from the room... but heat transfer happens faster in direct airflow than it does in stagnant air. Especially on something that transpires like a human or a plant (which is why fans feel cool on a hot day even thought its blowing hot air), but similarly so on heat sources like lights.
Airflow in and of itself wont cool the environment.. but directed airflow with smart exhausting can noticeably lower temps. It's the same idea as sucking the air directly off your HPS to exhaust. Your removing heat via heat transfer across moving air.
2x3 tent that exhausts into the 4x8 closet its in got up to 95°f under an HLG 260w diablo with nothing but the exhaust fan running. 1 fan blowing at the driver and 1 fan pointed at the boards had temps 77-83°f dependent upon how long the light had been on.
Not to be argumentative, but I think the blanket statement that moving air wont cool a room isnt entirely true. If I turned my exhaust off and had just 2 fans.... I'd be lucky to see 94°f, sure.. but air movement in conjunction with exhaust surely has cooling capability to an extent beyond simple exhaust.. dependent upon heat source, room size, airflow, and the multitude of other things that effect the environment of a closed space