It should we have 2- 10 cylinder 2 stroke engines at work that have turbos they are 2000 hp each and run at a smoking 330rpm day in and day out.
The big problem I think will be the cost for a turbo and then the oiling system
to keep the turbo happy. I'd use a tuned exhaust pipe instead lots cheaper and a lot easier to install.
Turbo charging a two stroke would likely be quite expensive and turbos need to be sized and matched to the application. Flow maps charted etc.
If you could find an expansion chamber it would likely perform like a turbo charger and cost less than $75 bucks.
We have a thread regarding expansion chambers and I've tried to post it full of resources to understand how they work and even softwares to download and design with. (should you want to try to build one....but you can buy one that will work for about what it would cost to try to make one)
Turbos can be set to boost at a specific rpm range. Expansion chambers can be
purchased that do the same for so much less. Less cost, less weight, less headaches, less time working on and more time riding, and that kinda stuff.
I always figured we used turbos on 4 cycle engines cause you couldn't use expansion chambers on them.