Of course, there is a reason why existing supersonic airplane designs do not use winglets in the same way that an airliner wing uses winglets. I imagine the parasite/wave drag penalty from a winglet would far outweigh any potential lift-induced drag reduction for a supersonic aircraft.
But for the sake of a thought experiment, would a winglet affixed to an airplane in purely supersonic flow be able to carry out the improvement of spanwise lift that it does on a subsonic wing?
Since the air pressure signals cannot travel upstream in subsonic flow, does this mean tip effects are not present when supersonic? Or are they still very well present because the pressure doesn't have to travel upstream, rather across the flow stream in order to still create tip effects?