I stongly advise pulling the engine and turning it upside down as Pro116 and others suggest. I would then turn the crank easily to ensure that all debris falls out. Compressed air, and gasoline bath can also help chase debris out. Be careful when turning the crank to not jam any debris or scratch your rods or pistons. Treat it like mom's good china.
Remember that on a 2-stroke engine, the fuel charge (air/fuel/oil) flows through the area that you have debris in. If you run it without getting all of this debris out it will end up in a combustion chamber and likely "blow" the engine.
I also am concerned on how you broke a piece off. This is a no-no when assembling an engine. Something just isn't right with the picture I am getting from reading your post. Maybe actual pictures might help get some good advice.
Remember that on a 2-stroke engine, the fuel charge (air/fuel/oil) flows through the area that you have debris in. If you run it without getting all of this debris out it will end up in a combustion chamber and likely "blow" the engine.
I also am concerned on how you broke a piece off. This is a no-no when assembling an engine. Something just isn't right with the picture I am getting from reading your post. Maybe actual pictures might help get some good advice.