Will dried buttermilk react with other ingredients in dry mix with oil, stored in fridge?
The baking soda and acid from the dried buttermilk should not react in any significant amount until you hydrate the mixture, so it should work.   Remember, baking powder is acid and sodium bicarbonate in the same can, and there is little except acid and reactant; your mix will have a lot of buffer ingredients as well.

I would not add the oil to the dry mix though until you are ready to make the pancakes, along with the water.