No, GC3 does not use the Nitrous engine.
Q: Is Galactic Civilizations III using Oxide's new Nitrous engine?
A: Stardock is thrilled about our strategic relationship with the talented team at Oxide Games, but Galactic Civilizations III is not using their Nitrous engine. Not because we don't think Nitrous is amazing – we've seen it, and "amazing" is a good way to describe it – but because we've been working on Galactic Civilizations III for a long time, and Nitrous is still being built. Galactic Civilizations III runs on a custom, in-house engine we built specifically for the game.