Amethyst buds that are on a budding amythyst block does not grow in ticking areas that are not loaded by a player. I don't see a reason why amethyst should not grow if crops grow and grass spreads within ticking areas.

Steps to reproduce:
1. Make a ticking area that has a amethyst geode inside it
2. Go so far out from the amethyst geode that it is not within the player's simultation distance (200 blocks should be enough)
3. Wait for amethyst bud to grow (on average it takes 136,5 minutes to fully grow, according to ilmango)