Can the ILS be shut down?
The ILS, or precisely the components localizer and glidepath antennas can be shut off, as they are electronic devices that emit radio signals. They can be turned off and on by ATC where required, e.g. having the same ILS frequency for two opposite runways and you only want one to be active at the same time or they can be shut down by maintenance directly at the emitters. ILS are usually not powered by UPS, so they will not be available during power outages.

If equipment is being shut down for maintenance or other reasons, you will see this mentioned in the NOTAM, such as here from Cologne/Bonn Airport, where the glidepath portion of the ILS runway 24 is out of service:

A4932/15 - ILS GP RWY 24 OUT OF SERVICE. 01 OCT 00:00 2015 UNTIL 30 DEC 00:00 2015 ESTIMATED. 
CREATED: 27 AUG 13:34 2015 


(Source: NOTAM EDDK)