It will completely dissolve, since it is not made of synthetic material. I used it as filter media once, and when I went to change the filter, I had only orangish crumbs left in the back of the filter!
So the answer is no, you can't...it's best to get open cell pore sponge from a craft store, or online if you can't find it locally. That is the only kind of sponge that will hold up for sure and that is suitable for this kind of project.
I actually have some, if you want - see the prices in this thread:
http://www.aquariacentral.com/forums/showthread.php?231686-Tons-of-stuff!!-Sponge-filters-air-supplies-foam-auto-feeders-Shipping-34479
Honestly, those XY sponge filters from eBay are so cheap, I can't see it saving you much mula to build your own!