So what you're essentially asking is – can photosynthesis effectively filter an aquarium?
Yes.
But could you fit 75 mangrove trees in that sump?
Mangroves do not metabolise as fast as chaeto & wouldn’t remove as much inorganic nutrients in a given time. This could be critical, depending on the fish load. Chaeto will certainly remove NH3/4 & NO3 & PO4. When illuminated on the opposite cycle to the display chaeto will maintain a good pH by removing the carbon atom from CO2, leaving O2 & oxygenate the water.
I only run an algae scrubber & some activated carbon. pH is always = or > than 8.1 PO4 0.03 NO3,,, zero if I wanted, in a heavily stocked tank (according to some

)
This is a green acropora in my tank over about six months