You would need to sand and stain not just a coating.

Well, had a suggestion to sand, (which I have been), wood bleach and let dry, stain w/country white (1 coat) dry. Ultimately staining with the tone of grey that you wish letting dry and then the polyurethane will not change the color of grey but will bring out the warmth of the wood without a yellow/brown. Thank you for your imput!

When working in the white/grays with wood, please work with a "clear coat" polyurethane that is water based. Oil MODIFIED will yellow the finish. Oil based will turn orange. A water based poly that is non-yellowing is what you are after. Be sure to allow the stain is allowed to dry completely (some of these stains require 4 hours...some require 21 days...be very aware of what you are playing with when it comes to cure times).

Be aware that oak has tannins that have a tendency to "bleed" into paint/white wash. This shouldn't be too bothersome as you are looking for a "warm" gray. The tannin bleed is often random and not considered uniform. Tannin inhibitors can be added to oak to reduce/stop this problem.