If the softener is working correctly as I assume it is doing (TDS <10 ppm from the tap), I don't think that would be it. But I could be wrong!!!
The softener only uses salt to clean the resin tank during the cleaning cycle. Once the cycle nears its end, the tank goes through multiple flush cycles to remove any remaining salt. Hopefully, my tap water is only coming into contact with clean, salt-free resin beads.
Is there any way to test your theory?
No idea how to test that. I know when I lived in a house with a softener, I would use untreated water, just to be safe. No science, just precaution.