I've never been to Captain's Grille for breakfast, but I have been to the Wave….
No, there is not an omelet station at the Wave. However, you can ask for eggs made-to-order, but it may or may not include an omelet. Wave's buffet feels like an after-thought behind in a vestibule.
Omelet station is available at Fresh inside Dolphin. You even get/give the ingredients yourself to the cook selected from a fixins' station.