It is possible to have a tank system without air pumps. I have never run an air pump on my tank, except for battery powered air pumps during power outages years ago. A whole house generator took care of the need to keep BPAPs around. Even without air pumps, my tank is well aerated with a closed loop mechanical filtration system powered by a Reeflo Hammerhead pump and with a venturi return nozzle that spits out air. There is swift, turbulent flow in the tank.
However, if I had a quiet, calm tank with not much flow action, I would definitely have an aerator of some kind and I would run it 24/7.
However, if I had a quiet, calm tank with not much flow action, I would definitely have an aerator of some kind and I would run it 24/7.