Properties of potassium carbonate as leavening agent
I've never heard of any preservative effect of potash, the reason it is still used in traditional recipes is the ashy flavor it imparts. That smokiness is not to everyone's taste, baking soda is a perfectly good substitute if you prefer the end result.  

You can refrigerate baking soda leavened cookie dough for 3-5 days without issue, it's batters where this would be a problem, but it would be whether you used potash or baking soda. The reason is that any chemical leavening agent starts to react with acid right away and produce carbon dioxide. Refrigeration slows this process, but doesn't stop it - cookies don't need as much leavening so it's not an issue whereas for a cake it's a problem. 

Refrigerating a spiced dough for a couple of days is a good step because it lets the flavor of the spices come out and blend. You can achieve the same thing by mixing the spices with the butter and refrigerating the butter for a couple of days instead, the end result is the same from a flavor point of view.