I doubt that would work - you would need to acid-treat the rust to dissolve it. However:
Once the iron forms rust it should be in the form of solid particles of a size that can be filtered out by a sediment filter. If you don't already, you should have a sediment filter before your water softener.
72g bowfront planted, CO2, 4x - T5HO, Eheim 2213 and 2217, 2 angels, pristella tetras, blue tetras, betta, albino bristlenose pleco, albino cories. Sword, vals, hygros, ludwigias, java moss and fern, anubias
2g Mac-quarium. Clown gravel, fluorescent plastic plants, and 2 guppies.