There is like no precedence for such a thing I’m aware of.
I work with sensitive biomolecules at work and universally they are more stable at -20c. Only large biomolecules like whole proteins can be damaged by freeze thaw cycles.
VitaminC nor B6 would be damaged by freezing.
If you are buying turmeric root, you could try planting one.
I have a 2+ year old pot of turmeric. I put it outside in the Spring and it grows, bring it indoors in the Fall and it eventually dies back. I dig down and cut off a piece of the root when I want some plus the leaves are edible. The moist soil preserves the live roots while the plant is dormant.