Vengance's class, or at least the project that led to her, was probably not secret. What the ship could really do or was meant to do probably was.
If it wasn't secret, why does Scotty, a character who happens to know about the Enterprise even before her first mission is so shocked at the sight of it? If the Vengeance isn't secret, why is it being built at a secret location around Jupiter? And if the ship was built years ago, why does Khan say he designed it and that it's designated as a Dreadnaught class as though it was the first time the ship was ever brought up? If it's not a secret ship, shouldn't someone be able to pull up the schematics of it like Spock Prime did with the NuEnterprise schematics onboard that torn up shuttle on Delta Vega?