I think the jury is out when it comes to whether it works as a mild chelator, or not. Perhaps it is recipe-dependent? When our last house had somewhat hard water, I noticed less soap scum from the soaps with vinegar, when comparing with those that did not have vinegar. So my experience is anecdotal at best, but seems to be shared by a few other soapers, as well.
People sometimes wonder if household chemicals can be effective chelators for soap. Possibilities include table salt (sodium chloride), sodium ascorbate made from Vitamin C (ascorbic acid), sodium acetate made from the acetic acid in vinegar, and sodium lactate made from the lactic acid in fermented dairy.
Sodium acetate and sodium lactate are two household chemicals that can indeed function as chelants. They are sometimes used for that purpose in foods and medical treatments.
I do not see acetate and lactate being recommended, however, as chelants in soap or cosmetics nor for treating minerals in hard water. The chelators normally suggested for these purposes include EDTA, citrate, gluconates, GLDA, etc.
So my take on this is not every chelator is effective for all purposes. Acetate and lactate should be used in soap mainly for the other qualities they contribute, not for their chelating ability.