Sure, but:

a) Now your singleton is also responsible for providing a mock implementation of itself (which shouldn't really be one of its concerns).

b) You didn't really do anything here: the class under test is still going to use the concrete implementation of C. You need a way of providing a mock implementation to your class while testing. The obvious answer to how to do it is dependency injection. But if you're going down that route, you can just ditch the whole singleton thing, instantiate a class using "new" somewhere else and pass it to your class. And in your unit test, you simply pass the mock implementation. This is what DI containers like Spring do. We'd be doing the exact same thing here, only manually.