From an http://www.ausgamers.com/features/read/3526651, it looks like idTech has already been considered and rejected as not suitable for games like Skyrim or Fallout, but they have had advice and assistance from id's software engineers when they thought they needed it.
Personally I doubt if changing the game engine (which part of the game engine?) would do anything to address the issues they have with animation - unless the Havok Animation Studio middleware is notoriously poor? If not, then it's what they're doing with the engine that people have a problem with, not the engine itself.
Remember, the so-called Creation Engine is a whole suite of in-house components and third-party middleware, and I'm not sure that there's one single part that's remained unchanged since Morrowind. We don't even know yet if they're still using for Fallout 4 the customised and extended model file format which was originally based on NetImmerse. But even if they are, that says little about the code that's making use of that model format.