No, the ILS is the same bit of kit regardless of the category but there could be certain parameters not met which would preclude its use at Cat II (or III). This is why you sometimes see ILS NOTAMed as 'Cat I' only. In addition, as Rabbs alludes to, there are factors outside ILS which may affect whether an approach can support Cat II, even a temporary obstacle inside the Localiser Sensitive Area for instance.
But to answer your question, no there isn't a separate bit of ILS that is switched on for Cat II.
HTH