The engine on the John Deere speedster I posted photos of here a couple of days ago is a two cylinder flathead with an updraft TSX carb. The engine originally came from a small pull type combine or small tractor, and thus has a governor which I have hooked up. I was showing it to my mechanically inclined BIL and brought up the possibility of disengaging the governor and hooking the accelerator pedal directly to the carb throttle valve in a more car-like fashion. He told me if I do that, with the updraft carb with no accelerator pump, I will be killing the engine frequently because it won't be reactive enough. Is this true? Photo below show the engine in its natural state.
I would say no, no change in performance and no stumble. Your engine is basically a heavy duty version of a Briggs and Stratton low performance industrial engine. It has very low fuel demands and low power production. Also I would expect a very heavy flywheel. It won't accelerate quickly enough to need an accelerator pump. All the governor does is limit RPM, it will still slam the throttle wide open when you ask it to. The only advantage I can see to bypassing the governor is removing the top speed limit by not letting the governor control maximum engine RPM.
The first mechanical accelerator pump came out circa 1932. There were some "syringe pumps" in operation by about 1921; however, the output of the syringe pump was maybe 5 percent of that of the mechanical accelerator pump. Virtually all updraft carburetors THAT HAVE ACCELERATOR PUMPS use a vacuum pump rather than a mechanical pump. The pump reacts to the lowered engine vacuum after the throttle has been opened. Never really considered what percentage of updraft carburetors have accelerator pumps before; but it isn't very high. Lots of updraft carburetors with no accelerator pump were used on non-governed engines. And that picture needs to be in living color. Everyone knows that all real tractors are painted green and yellow! Jon