There are two kinds of diffusion, turbulent and molecular. Both occurring in water. Molecular diffusion is almost just an idealistic concept, but is important in a few instances, primarily being water movement in interstitial water in sand and rocks, it is very slow movement but is important for nutrient transport through sediments(not being stirred by organisms).
Water movement in the interstitial space in sand, soil, etc. is due to gravity, it is not advection. What is dissolved in the water moving due to gravity, is being advectively transported. By the way, the notion of advective water movement is wrong, and in contradiction to the sciences, and the definition of advection/advective transport.
It is completely wrong to say that water does not diffuse or move by advection. The best example to give is the Gulf Stream, it is the mass advection of a water mass through the ocean(like the return line from a sump), and along the side of the stream the gulf stream water diffuses into the waters surrounding it. If you did not have diffusion in an aquarium you would have no mixing or anything.
The Gulf Stream is driven by the prevailing winds, not advection.
Diffusion is the "movement" of a solute within a solvent, from an area of a higher concentration of the solute, to an area of a lower concentration of the solute. Water is the solvent, what is dissolved in the water is the solute. Water does not diffuse, this is straight out of the text books—check it out...
Advective transport (again right out of the text books) is the movement of of a property or material due to the movement of a fluid medium. Or, to relate it to above, the movement of a solute due to the movement of a solvent.
Since water is always a solvent, (the universal solvent) and not a solute, water does not diffuse, and it cannot move advectively. Such beliefs are contrary to all the sciences, and torted by folks with little to no background in physics, or with the intent to mislead...The only time water will diffuse is across a semi-permeable membrane in a process called osmosis. This information is availble in lower level Biology courses, and even wikipedia...
Ocean water movement is caused by interaction with the atmosphere e.g. air currents commonly referred to as wind. Since the ocean water is not dissolved or a solute within the atmosphere, (nor is it a solute or dissolved in the ocean water...) this motion is called a current, not advection.
ADVECTION:
noun
noun:
advection
- the transfer of heat or matter by the flow of a fluid, especially horizontally in the atmosphere or the sea.
It may be that the engineering definition of advection and diffusion is not happening, but the scientific definitions are absolutely at play in an aquarium.
"In physics, engineering, and earth sciences, advection is a transport mechanism of a substance or conserved property by a fluid due to the fluid's bulk motion."
I am sorry, but engineering is a science, and uses the same definitions as every other science. I don't like bringing bad news, but the science/engineering does not change, nor do the laws of physics get thrown out the window, because it is an aquarium.
"The term advection sometimes serves as a synonym for convection, but technically, convection covers the sum of transport both by diffusion and by advection. Advective transport describes the movement of some quantity via the bulk flow of a fluid (as in a river or pipeline)."
E.G. advection is NOT a synonym for convection.
As to the question at hand, having a sponge coated in a thin layer of DIY dry rock, you would create a larger more porous center and the possibility for more bacteria to inhabit it. It wouldn't really pick up any more detritus than normal live or dry rock, it would just replace the center of the rock which would take years and years to have water seep into and become useful. Once you were able to get bacteria to inhabit the sponge it would likely act just like bacteria inhabited dry rock or ceramic media.
First you have to evaluate how there will be a bulk movement of water through the "sponge rock" at precisely the right speed, for denitrifiction to occur. Since advective water movement does not exist, what is the motive force for the water to advectively transport nutrients through the rock at precisely the right speed, and are the "pores" small enough so the flow is low enough that oxygen levels drop the right amount...
Lacking that, you need to evaluate whether diffusion alone, will provide the "processing power." Remember water does not diffuse, except across a semi-permeable membrane (osmosis

the sponge and shell are not semi-permeable membranes. And if they were, the water would diffuse through, certainly, but from an area of lower concentration of solute, to an area of higher concentration of solute, or not at all if solute concentration is the same on both sides; what was in the water, would stay behind. Semi-permeable water will pass, but nothing else.
If neither can be present, then there is also no convection these things can be attributed to. These are the same things that put natural rock in question, and it is glaringly obvious that rock does not provide any significant denitrification: Otherwise, there would not be such a vehement search for something that does do the job...Every tank these days has more than enough rock in them..... 2 + 2 = 4, not 5, not 3.