What is the behaviour of ILS when there is an unmodulated interfering carrier signal?
If an invalid signal is received, then it must be modulated since it is only by measuring the modulation, that the receiver knows if the signal is valid and where it is relative to the localiser and glideslope. An unmodulated carrier on the same frequency is additive.  

An unmodulated carrier on a different frequency will not affect the receiver (ignoring possible harmonics of course). 

I suppose that if you could increase the power enough, an unmodulated signal might cause the signal to noise ratio to drop so low that the failure flag would show.