The sponge would provide surface area for good bacteria to grow. but honestly, qts are temporary for the most part, so a lot of us just rely on water changes to keep parameters in check.
Ammonia is constantly excreted, probably at a higher rate when they are stressed (most do, but it depends on the species), so some active bio-filtration is very much called for in QT.
If you're in a hospital tank where you'll be medicating, that's a different story. Water management is totally on you in that case. :)
You don't want to expose a potentially healthy fish to any concentration of ammonia if it can be helped. <1 ppm can have toxic effects...
An interesting quote: (highlighting is mine, but that's not the only interesting part...too bad the whole article is not available)
http://www.sciencedirect.com/science/article/pii/S0025326X02002278
Present ammonia criteria for aquatic systems are based on toxicity tests carried out on, starved, resting, non-stressed fish. This is doubly inappropriate. During exhaustive exercise and stress, fish increase ammonia production and are more sensitive to external ammonia. Present criteria do not protect swimming fish. Fish have strategies to protect them from the ammonia pulse following feeding, and this also protects them from increases in external ammonia, as a result starved fish are more sensitive to external ammonia than fed fish.
Ammonia sensitivity after starvation makes reason #4,752 why our new fish are so sensitive after arriving from the supply chain. Not sure if feed is offered at all during this phase...and it's hard to imagine any fish eating at this phase anyway...so I'm sure they are mostly/all starving.
