OK, I am one of those curious soapers who always says, 'I wonder what this will do?' (Just ask anyone here lol)
So, I HAVE used my dehydrator on the lowest heat setting on a batch of each recipe I make, to see what differences, if any, it made in dry and cure time.
Soooo... It did help with drying them out quicker, but you have to make sure to put them farthest away from the heater, even on the low-heat setting, and keep an eye on them once or twice a day, no more than 2 days, or they will either warp from the heat, warp and maybe even crack from too-fast water-loss, and they'll even 'cook' and get crusty dark edges if they're smaller bars too close to the heat or if left in there too long. And if the heat is too high, you'll gel -- or re-gel -- your soaps turning them into a runny liquid mess!
Any higher than 95 degrees F and they'll get gooey or they'll overcook depending on your soap recipe. Think soap-jerky lol. Perfectly usable but ugly. Was an interesting experiment in trying it out though.
My conclusion was -- it dries them out quicker if used with great care, which might allow you to store them sooner while they complete their cure. Because drying out is only part of the cure, just like with HP, they still didn't reach their full potential with mildness and lather until they'd cured for 4-8wks. And you can usually help the soaps dry just fine with a normal fan to help circulate the air.
I do still use it with my HP carrot soap which has a high water content, to help keep good dry warm air circulation, because otherwise it takes months to dry and get hard. Just the nature of the recipe, and I like the end result too much to change it lol.
Ummm... don't ever put cut 'bars' of songwind's shave soap recipe --the full KOH version-- in a dehydrator. It will not dehydrate, it will soften and spread out like cookie dough in the oven. LOL