No. I wasn't concerned with the issues of handling heirarchical Z - that's an extra problem. You can do early Z tests with a bog-standard Z buffer.
Then I still don't get it.
Early z test meaning test before shading/texturing/etc?
Unless your shader writes to z, you can always do early z, right?
Whether you have alphatest or not, if the z is greater than what's in the zbuffer, the pixel will not be visible, so it is not necessary to perform any alphatest at all. Only if the z-test passes, you have to do the alphatest.
So without a hierarchical zbuffer, I don't see any kind of problem?