Whenever there was positive inlet pipe pressure, there should be quite decent scavenging of the combustion chamber, so it should two-stroke nicely. However to get positive intake pressure it would have to be running full-song, and would have two-stroked anyway.
Supercharging two strokes can be beneficial, but only if they have the right intake and exhaust timing. The only practical cases I've seen that worked well had pressure lubrication of the engine and did not use crankcase induction. Take a look at a traditional Detroit Diesel: camshaft-operated overhead valves, and a Roots blower to handle the intake chores, but it ran as a 2 stroke. In other words, just build it like a 4 stroke but run it as a 2 stroke. In practice there has been at least one mass production piston-port controlled supercharged 2 stroke diesel that worked pretty well, but like the Detroit Diesel, it had pressure lubrication and did not use crankcase induction. That engine is the Commer TS3, often called the Commer Knocker for the obvious reason - its diesel knock was awesome.
Both of those engines used a Roots blower to push air into the cylinders, instead of using either crankcase induction or piston-generated suction.
