If a runway was lost and it was expected to be short term, then yes, the ILS would probably stay on. It makes it easier to bring the first few in if you don't have to wait for the ILS to get up and running.
However, it should be borne in mind that sometimes an ILS may be radiating at the other end for test purposes or whatever, but this does not mean that the runway is NOT available in an emergency.
The T5 works do throw a spanner in the works and this was highlighted at a recent TRUCE when some BA guys were shocked to find that the NOTAMs don't provide nearly enough info on crane erection (tee hee) times. Food for thought if you're about to commit.
P7