You could , Benefical Bacteria needs surface area to grow and live on...but you would probably restrict the water flow. Also by removing the Blue Filter media (the Filter cartage) you would probably lose the ability to remove the Fine Particle stuff that could make your water cloudy.
You plan to keep the Gray Plastic Inserts in correct and remove the Filter Media with the carbon?
I would cut out the Carbon out of the Blue Filter media and in order to give you room between the Blue Filter media and the Gray insert and stick the Terra cotta there. You could use a cheap mesh bag or pantyhose....
60 gallon(Parrots and Convicts) 55 gallon African Cichlids 5 gallon Betta tank 35 Gallon Hex (Bolivian Rams, Oto cats, Bloodfin Tetra and a shoal of Tiger Barbs) 75 Gallon Oscar Condo. 30 gallon GBRs & Danios