Crankcase scavenged two-strokes, like the ones in chain saws, hate exhaust back pressure. That's why turbocharging is not feasible for them. Actually, all piston engines hate exhaust pack pressure, but with an Otto cycle (four-stroke with valves over the piston), the higher exhaust back pressure from the turbine side is compensated almost completely by the increased intake pressure from the compressor side, so that the engine still runs like it should, mostly anyway. There are still some changes, like the need for shortened overlap of intake and exhaust events and shortened exhaust duration, generally. But these changes are easily made and can mitigate most of the problems that exhaust back pressure would normally cause.
The Otto-cycle engine depends somewhat less on the kinetic energy of its operating gas to charge and scavenge the cylinder than the crankcase-scavenged two-stroke. A crankcase-scavenged two-stroke uses a gas at a low pressure and depends mostly on velocity to get the charging/scavenging jobs done. An Otto cycle can vary the proportions of pressure and velocity to suit diffierent conditions, by changine valve timing. This can be changed somewhat with a two-stroke with port timing, but not nearly to the same extent, and the adiabatic losses will always be greater since the two-stroke engine favors a low-pressure/high-velocity type of flow.
On top of all this, the crankcase-scavenged two-stroke engine has lower peak exhaust temperatures. The turbine is essentially a heat recovery device, so with less heat available in the exhaust, the turbine has less waste heat to work with and consequently spins slower. In selecting a turbo, when it is found that a particular turbo will spin too slow, the general solution is to install a smaller unit, or one with a more restricted turbine inlet (lower A/R ratio). But this produces more back pressure, possibly compounding the problem.
Both port uniflow (Cooper-Bessemer, Fairbanks-Morse, etc.) and valve uniflow (Detroit Diesel, EMD) use turbocharging successfully. Note that these engines ALWAYS use pressure aspiration with a positive displacement pump as part of their design, even when a turbocharger is not used. So when a turbocharger is used with a uniflow two-stroke engine, it still has a seperate positive displacement scavenging pump, so it has both a turbocaharger and a supercharger. These engines will not run without pressure aspiration as there is no scavenging/charging force otherwise.
Crankcase-scavenged two-stroke engines have been successfully turbocharged, but success depends on the ability to carefully match the turbo unit with the correct event timing. In an Otto cycle engine, you can easily make even very radical changes to the event timing by simply changing camshafts. It's not nearly that easy with a crankcase-scavenged two-stroke; you wind up havig to make new cylinders.
Crankshaft-driven supercharging can be more easily adapted to small two-stroke engines, but lacks the advantage of consuming some engine output to drive the pump, whereas the turbo uses waste heat from the exhaust. This is not a trivial amount of power; in a truck diesel engine for instance, more than 50HP is dissipated across the shaft of the turbocharger, so a shaft-driven supercharger of similar capability would have to subtract that kind of power from the crankshaft to get the job done.
Jimbo
You would have to have a real high volume blower with a fast acting waste gate.Any thing is possible,however it may not be practical. 
