Is this tank cycled now because there is cycled filter media in it?

Yes, in an absolute sense. A tank doesn't cycle, just the place where the bacteria colonizes. A tank is "cycled" when it has a means to oxidize ammonia into nitrate before it is able to build to harmful levels. Your tank is cycled in the sense that some level of animal life can be in there and the bacteria in that sponge will be sufficient to process their waste. Now, what kind of animals and how many is another matter. Really the limiting factor is the lack of water flow through the sponge, so the ammonia the bacteria consume will only be that which diffuses into the water surrounding it. So you probably couldn't have a lot of fish releasing a substantial amount of ammonia.

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