Yes, the ACV does remove minerals from the scalp. It also closes the cuticle for better moisture retention, and restores the pH which is important because the bars are alkaline but hair is slightly acidic.Many curlies who do not use poo bars still rinse regularly with ACV because of its other benefits.
As this article notes, it is impossible to make a pH balanced shampoo bar.
The Efficacy of Shampoo Bars | Curly Nikki | Natural Hair Styles and Natural Hair Care
If you do not have hard water (i.e., high mineral calcium content), you may be able to skip the rinse.
I use the bars 3-4 times/week, and ACV once a week. My biggest concern with the vinegar was the odor, so I made an infusion with herbal teas from CV - smelled awesome and left my hair super shiny. Others have recommended lemon and/or orange rinds and hibiscus leaves (h/t Keihs), I haven't tried those yet but they'll be in my next ACV.