You will not burn up the solenoid by not tapping the throttle. As long as the metal plunger is in the center of the coil of the solenoid, it will be fine. It will not hurt it to be pushing on the throttle, but not being able to physically move it.
Which brings up a question on the original post that started this thread; From his description, he starts the engine normally, it idles normally, and then revs up to 2100rpm. How can that be? We all know the solenoid doesn't have enough power to open the throttle by itself. So why is the engine rpm flaring up on it's own?
I also believe the best way to set the high idle speed would be with the engine fully warmed up. The initial rpm is drastically affected by the temperature and the viscosity of the oil you are using. I don't have mine hooked up, but I can hold my foot steady on the throttle, and as the engine runs for a few minutes, it's going faster and faster at a gradual rate as the oil and everything else warms up.