yea it will stop charging after a while and run off of the charger until you unplug it.
i did learn something about battery cycles the other day though...it pertains to notebooks but im sure the batteries have the same technology. if you fully drain your battery and then recharge it completely that equals one cycle. also ifyou let it go down to half way, charge it, let it go down to half way again and then charge it that is also one cycle. now i dont know if this is as good as a cycle as a complete power drain but it very well could be
-chris