Whenever you max Piety it causes all Holy Sites to give an additional +3 gold and +3 culture. Whenever you max Freedom it causes all Great Tile improvements to give +100% yield.
No, Freedom does not interact with the extra gold and culture from Piety's improved holy sites. As you can see from the following screenshots I've maxed out Piety and Freedom, but the culture and gold yield are not increased.
This is probably because the Piety bonus does not count as part of the base yield, which is what Freedom improves.