The only thing I can see that vinegar would do as a softener is removing detergent or other residues. I use vinegar for a lot of things. It will clean car grease off walls; it was fresh car grease and if it's been around a while I don't think it would work. Baking soda in a drain followed by vinegar can help keep it draining. I need to clean my shower head with vinegar. I use it to clean coffee pots. I have a spray bottle of water and vinegar that is my first go-to for cleaning up lots of things. AND it helps get rid of the smells I don't want to smell. If I'm turning into skeeter bait, I think I'd be able to live with the dryer sheet smell just fine.
This is the last time I'm frogging this project for the last time.