I used to frequent an LFS
about 20-25 years ago (wet dry filters were taking off at the time) and they used this type of setup in a lot of their larger tanks. Have not been back there in a while so I don't know if they continued to use them. I have seen this setup in pond/aquaculture systems.
This would work, however, there are a few things to consider. You would want to prefilter the water so that solid waste is not added to the bio media. Else you would encourage the growth of heterotrophic bacteria (I believe bacteria in the nitrogen cycle are autotrophic). If you are growing plants in anything above low light conditions, a portion of the injected CO2
would be removed with this setup.
Otherwise, for ammonia/nitrite processing this should do. Good luck. Record your water parameters so that you can see how effective this is.