Well… I say NO!
A user story can be a perfect short description of the use case, but it does not contain all the details you need for implementing, testing and maintaining the software.
A use case describes the what of the user story in much greater detail. And as a requirements engineer, when writing a use case description, you are forced to make it thoroughly logical – with no open ends.
So… user stories are great to uncover the who and the why, but you still very much need use cases to describe the what.