ceramic rings inside tank.

Bacteria is present in most surfaces in your tank. Substrate, decor, and even the glass is a host to some bacteria. Your filter is in an area of high flow, which provides oxygen to sustain the bacteria in adequet numbers. In speculation, I would think the gunk trapped in your mechanical filtration would also suply additional amonia as a food source. If you are asking if you can ditch your filter for bio-rings in the substrate I would say no. If you want to add them in the hopes it would add more bio-filtration, I would say it will work on a small scale, but the cost would not be worth it vs. adding the rings to your filter.

IME, I would say that there is a lot of bacteria in the tank. I have put on a new filter with out any kind of "cycling" of the new filter and didn't have any ammonia/nitrite spikes. I have also removed decorations, and have gotten nitrite spikes. Maybe it just depends on how you do things. My old filter I changed the cartridge every month, so the bacteria probably built up in the tank since it was always being removed from the filter every month. I now have an aquaclear, and instead of replacing the sponges, i just squeeze them out once a month, and rince out one the sponges every other month in hot water to clean it. (I have two sponge in the filter and alternate which one I clean). I suppose I would get a numbers spike if I took the filter off now.

As far as the rings go, yes they would help. Ceramic is porous and would provide a lot of surface area for bacteria. That being said, you shouldn't get rid of the filter. It does way more good than a few rings would. If anything, it provides water movement which would move the water over the rings.