Joshua Bloch aconselha contra isso em seu livro Java efetivo :
That a class uses some constants internally is an implementation detail. Implementing a constant interface causes this implementation detail to leak into the classes exported API. It is of no consequence to the users of a class that the class implements a constant interface. In fact, it may even confuse them. Worse, it represents a commitment: if in a future release the class is modified so that it no longer needs to use the constants, it still must implement the interface to ensure binary compatibility.
Você pode obter o mesmo efeito com uma classe normal que define as constantes e, em seguida, usar
import static com.example.Constants.*;