I don't know if it'd be worth the bother. It could be done but I don't think you'd improve the performance by that much. The problem with a crankcase scavenged two stroke is that the exhaust gases are still escaping when the piston is on it's way down and taking in fresh air/fuel mixture. This means that some of the air/fuel mixture escapes out the exhaust port and by turbo/super charging you're forcing more in AND more out. Sure, the pressure waves in the expansion chambers push a lot of it back in but the chambers are only tuned to do that at a certain rev range (read power band). Anyhow, carbs and turboing ARE a bad idea - very troublesome to fit an intercooler (without one the engine is prone to detonate) and you end up with fuel atomisation problems.

Another point to consider is the crankcase seals on boost and if they could take it.

Certainly though turbo/supercharging a two stroke IS a GREAT idea but it would require a rework of how a crankcase scavenging two stroke works, namely, doing away with it and going to a valve system similar in function to a four-stroke. Direct fuel injection and variable valve timing are high up on the priority list too. How I envision it working is when both valves are closed, air and fuel are forced in to the cylinder. Piston travels up to TDC and fires forcing the piston back down on its power stroke and the exhaust valve opens. Some spent gases leave due to pressure. Shortly after, the inlet opens _while the exhaust is still opened_ but only air is forced in to the cylinder to evacuate the last of the exhaust gases (as remember, we are missing an exhaust stroke to push out the spent gas) and to aid in cooling. Shortly after, the exhaust valve closes, the pressure builds in the cylinder and fuel is forced in, leaving as back where we started.

I think this is similar to how the old diesel supercharged two-strokes operated. No need for expansion chambers, sadly, as no spent fuel is escaping but it would be a highly efficient engine if someone got it to work. I'd say it'd be easier to play around with a banshee motor as parts are more common and cheaper, and either way you go you're sure to shag a cylinder and maybe a rod occasionally experimenting and we don't want fewer parts available to go around

Other interesting concepts on how to get valves operating is using a servo operated open pipe that has a hole cut in the side of it like a flute (someone mentioned somewhere that Norton used this design early on). The flute hole would line up with the exhaust port to allow gases to leave. This would eliminate energy spent lifting valves against springs and friction on cam shafts and turbulence. Best to have the inlet valve in the top of the head as in a four-stroke so that air can be forced in the top evacuate the exhaust sooner. Two stroke exhaust port position could be retained.

Anyway, just some ideas I had. Seems if your friend has the setup to do serious work you may as well take advantage of it and do something really impressive. Fuel injection is the way to go if there is any chance of seeing two strokes out side of museums in ten years but fuel injection without a different means of scavenging seems to be wishful thinking.
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MC21 Honda NSR250. TYGA 300 conversion.