From my experience, the only thing that will suffer in a carby that sits idle for long periods is the rubber diaphrams in the accelerator pumps and any O-rings that are normally exposed to fuel.
Run the engine to temp once a week or so and that will keep them immersed in fuel.
But beware of acid build-up in your engine oil though, especially from repeated short runs of the motor. You may want to change that on an even more regular basis.
In fact, acidification of the engine oil is of much more concern than the carby.