Running without a header or a loose one in this case, can give you great performance from the engine. BUT it is bad for the fuel economy and the overall life of the engine. The purpose of the exhaust systems on these tiny giants is to allow for a more complete burn of the fuel and oil within the cylinder of the engine. When the engine combusts, some of the oil and unspent fuel get ejected with the exhaust gas. Backpressure from the pipe and manifold push most of that stuff back into the engine for another burn. That is the way the engine is supposed to run.
NOW, you take the manifold and pipe off. You get a mess around the rear of the engine...but the sucker sounds mean and runs like a raped ape. End result is poorly lubed engine that gets pretty darn hot...and eventually fries itself (we're talking over a tank or two...maybe more).
If you can afford to throw away the engine, run it the way you like it. I would, however, recommend keeping the pipe and manifold right where they belong.