Most likely, since the engine does somewhat determine the performance, much like how Kerbal Space Program used to get very intensive with crafts due to the way Unity was back then.
However, it still does rely on the developers mostly for the performance of the game, as if your hypothetical game is not coded properly it will run badly no matter what codebase you use.
However, a good engine and good programmers can double stack to make a game run extremely well... However even with a powerful engine such as RAGE (Rockstar's proprietary engine used for their modern games) cannot save GTA IV from running like crap due to terrible coding/porting