The only thing that D unittest do, is executing code if you pass -unittest to the compiler. What you do in this code is entirely up to you.
So, I think the answer is no. No you can't do this with the current language and standard library. When I started learning D, I thought the way D handles unit tests is very limited compared to libraries in other languages. However D makes it straight forward and simple to build something more elaborate. So what I'm doing now, is to register delegates as unit tests, so I can get a statistic telling me, how many pass and how many fail. I think it is doable in an similar way to associate test cases with classes and for every subclass look if a test case should be inherited from the baseclass using Ds compile time reflection capabilities.