With the frequencies used and the nature of the signal the distortions tend to be very limited.
Remembering that the localiser signal is generated by an antenna array beyond the far end of the runway, the main risk of interference is when a landing aircraft reaches the end of the runway and turns off. It is the effect of the aircraft turning (changing its profile) and moving off the centre-line that creates the distortion.
That distortion, while it may be observed as a wobble all the way out on the approach, is only likely to be critical for a landing aircraft in the final stage of approach - maybe the last half-mile.
While it is improbable that the distortion would be sufficient to destabilise the approach, I understand that normal practice, under low visibility conditions, would never allow landing sequencing to be that tightly spaced anyway.