Essentially ILS runs on batteries all the time with the batteries being constantly charged by the mains supply. During Cat II/III ops where there has to be less than a one second break during any power failure, generators become the primary power charge to the batteries with the mains supply being the back up.
In the event of failure of one of the supplies (mains or generator) once Cat II/III ops are in you are allowed to carry on for two hours (I think, need to check) before suspending them. However, you are not allowed to start Cat II/III with one supply u/s.
In Cat I where the generators are not running, it can take up to 10 secs to the generators to start and kick in.
CAP168 Licensing of Aerodromes is your bed time reading.
http://www.caa.co.uk/application.aspx?categoryid=33&pagetype=65&applicationid=11& mode=detail&id=232