Yeah you could use those sponges. People will big fish rooms use sponges bc it's cheaper to run a bunch of those off a giant air pump.
I use two sponges in my 125 using my powerhead. I originally didnt like the idea of running the powerhead unprotected but now I think it would be fine.
I recommend the Hydro V pro version. The regular has smaller pores and it's a pain to rinse it out. The pro has bigger.pores.and rinses much easier.
You can get them cheaper here but you have to factor in shipping (can also pick up for free if you happen to live by Gurnee IL):
Pro version:
Hydro Sponge PRO Aquarium Filters The Hydro-Sponge Pro is the newest product line among our family. The Hydro-Sponge Pro like the Hydro-Sponge is made in all the same sizes but unlike the Hydro-Sponge line it uses reticulated foam. This gives the sponge itself almost double the efficiency as...
www.aquacave.com
Regular one (one I don't recommend as it's harder to rinse. I have both this and the Pro):
Hydro Sponge Aquarium Filters The Hydro Sponge filters provides both mechanical and biological filtration. Aerobic bacteria colonize the sponge, providing a bacterial substrate to facilitate the nitrogen cycle. In addition, the Hydro-Sponge traps larger waste particles, mechanically cleaning the...
www.aquacave.com