It's hard to find anything like a schematic of a Nimitz-class carrier for obvious reasons, but as far as I can tell yes, it's all directly steam powered. The reactor boils (sea)water, which is used to power 4 steam turbines[1][2][3], those turbines drive the propellers.

You've probably seen aircraft carrier decks covered in smoke. This is because the Nimitz's catapult system is directly steam powered, service steam is widely used on the class. I can't find a citation for this now (this is from memory) but I saw some documentary on it once where it was mentioned in passing that even the washing machines on the ship were steam powered. There's service steam everywhere on the Nimitz.

Having steam power everywhere introduces a lot of complexities, which is why the Navy's moving away from it with their new carrier class[4]. The Gerald R. Ford-class does away with service steam in favor of more powerful electric generators. There'll be no service steam, just steam to drive the electric turbines.

1. http://www.nimitz.navy.mil/FACTS.html

2. https://en.wikipedia.org/wiki/Nimitz-class_aircraft_carrier#...

3. https://www.marinelink.com/news/dresserrand-propulsion302604

4. https://en.wikipedia.org/wiki/Gerald_R._Ford-class_aircraft_...