That sponge filter is a good idea but only if you clean it regularly. Many times mechanical filters like that will end up being nutrient sources and not sinks.
For me the idea of a qt is this: I use a tank, heater, and hang-on protien skimmer (a pump would work but I like the oxygenation of the p.s.) Because my qt is always fairly small, the p.s. provides circulation as well as filtration. The p.s. really does nothing because I have very little organic matter in the qt (i dont feed in my qt because of a lack of filtration). Water changes at least biweekly are very important here.
so with all of that to keep the corals alive, here is what I am doing this for. To me the glass of the qt is like a petri dish culturing bacteria in a lab. You make a sterile agar medium (the qt tank) and then add a culture (new corals) and wait for it to grow so you can study it. I qt for three weeks and check the glass often to see whats growing. Most pathogens can be seen on the glass. Also look for bacterial diseases and such on the corals. Dip as needed
I do agree that the colonized sponge would help with filtration and making the corals happy, but that can be done other ways. Adding this imo would make it more difficult to analyze my 'petri dish' because there would be much more going on. Plus I kinda like my filtration to be sub-par so potentially pathogenic algaes will 'show face'
hope this helps and opens your mind to the whole qt thing