I got a similar system sunk in much greater concrete bassin benearth the floor, covered with a thick steel plate. I would not run it open. For other reason too... But the system you refer to is totally enclosed. Furthermore in case it still would be too loud, what I don't expect, you could make a second, nicer casing from OBS or such, even will it with insulator material.

There still maybe the sound of the water in the upper draining pipe, so do not expect absolute silence.