Let us assume we have a localizer (identifier I-STK) transmitting at 110.10MHz and a matching glideslope at 334.40MHz. If a device aboard an aircraft tracking the I-STK ILS were to emit an unmodulated interfering carrier on either of those frequencies that is then picked up by the ILS receiver's antennae, with enough power to render the LOC or G/S signal unreceivable, would the pilots see a consistent wrong indication, erratic/wildly changing indications, or a FAIL flag? Would the behavior under this circumstance differ between glass and round-dial aircraft cockpits? Also, would the ILS Morse identifier be rendered unreceivable before or after the cockpit indications fail?
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.