I'm not sure about a Supercharger, but there was an after market company in England that had two different turbo conversions available for the SJ-410 when it was still on the market.
Apparently one way to build it is to have the carb mounted in front of the supercharger, so the fuel/air mixture is mixed before it is compressed by the supercharger. This gets rid of the problem with the fuel bowl not accepting gas as it is full of compressed air. But you can blow up the supercharger if the car backfires.
You would probably have to have a slightly stronger fuel pump in order to make sure you have fuel, and probably larger jets but I don't see why it wouldn't work.