Before I'd consider adding 6" of concrete to a deck footing, I'd first make an attempt to determine both the condition and depth of that footing. If it's too shallow (above frost line) or the concrete is suspect, then the better option would be to just completely remove and replace to an adequate depth. And an easier sequence for doing that is to temporarily support the deck adjacent to the post being replaced, yank the post and footing, dig the new footing hole to proper depth, tamp the bottom, then install the new post (with steel stand-off bracket having bottom anchor rod/fins, attached to the bottom of the post) suspended over the hole and attached to the deck framework. Final step is filling the hole/form with new concrete up to the bottom of the bracket, and of course removing the forms and temporary supports.
I've replaced a few deck posts in my day, and would never do it the hard way again (trying to scoot the post/anchor assembly into the tight-fit space created by the new concrete).