Since the question seems about aircraft theory, I'll answer with theory. The short answer is that anything can, and will fly given enough time and effort.
One of the biggest limitations for making a conventional configuration rotary aircraft fly at supersonic speeds is materials. When a rotary blade is inline with the path of travel, it has to withstand significant compression forces along its long axis from the shock. There are three solutions for a conventional configuration - bigger & stronger blade (heavier) new materials, or shorter blades (less lift).
If you don't mind deviating from conventional design, then introducing a shroud around the blades will allow you to remove these forces from consideration by allowing your shroud to absorb the forces of the created shock. You could probably reduce the weight of each individual blade by bracing it against the shroud, (think - beam braced at one end vs both ends) Since the air between a shock wave and expansion waves is sub-sonic. If you're lucky, and physics doesn't hate you, then you may get expansion waves behind the shroud, so your rotor blades will be in a sub-sonic medium. By pumping air from above the shrouded rotor to the underside, you cause lower pressure on top, higher pressure on the bottom, causing a pressure gradient and generating lift.
This is all speculation based on my limited aerodynamics knowledge. In real life physics usually hates you, and you'll get some really messed up expansion waves and shock waves along the inside of the shroud, coupled with some fugly shocks being formed by the rotor blades themselves. Since prototyping has become super expensive, and wind tunnels seem to be a dying race nowadays, this would have to be simulated with CFD, and as far as I know, CFD isn't that fast and accurate yet, which could explain why this hasn't been tried yet.