No, you need the physical switch to remain in the "on" position, always. If you want to turn it off manually, find the iHome plug attached to the wall, and press the little toggle button on the top-right (behind the little green light). Then, yes, "Siri" will know that the light is turned off.
Doing it your way (turning the lamp off at its built-in switch) will just make the lamp not respond to the iHome controller until you toggle the built-in switch again. This is two switches in series. They both have to be "on" for the light to get power; if either (or both) is off then the light is off. You are thinking of it as something like a "three-way" wall switch (when you have light switches on both ends of a hallway so that toggling either will toggle the light between on and off), which would be awesome but electrical outlets don't have the third powered prong which would be required to allow such fanciness (there is a third prong but it is for ground fault). So, that won't ever happen.
This is the fundamental issue with trying to retrofit home control into legacy "dumb" devices. You won't see the really nice benefits until the devices themselves are smart enough to understand home control.