Your thoughts in this filter setup

Sometimes the fluidized action can break up solids, and when broken up, smaller pieces are put into suspension so mechanical media can remove those small particles. But as stated above, it is primarily a bio filter, and can be a water chemistry reactor depending on what media is used.
I use aragonite sand as biomedia, and to aid in pH and alkalinity stability in mine.
If (and sometimes they do) pieces coagulate into large chucks, the efficiency of biofiltration is reduced, these chunks are sometimes called mudballs.
It is more efficient to put mechanical filtration before the fluidized bed to remove particulate, and use gravel vacuuming to remove larger chunks before they make your filter media a nitrate factory.