A project I am working on has a bunch of legacy tests that were not properly mocked out. Because of this the only dependency it has is EasyMock, which doesn't support statics, constructors with arguments, etc. The tests instead rely on database connections and such to "run" the tests. Adding powermock to handle these cases is being shot down as cost prohibitive due to the need to upgrade the existing project to support it (Another discussion).
My questions are, what are the REAL world tangible benifits of proper unit testing I can use to push back? Are there any? Am I just being a stickler by saying that bad unit tests (even if they work) are bad? Is code coverage just as effective?