Sure.
The VOR is sending out a dual-phase signal, the on-board receiver can detect which part of the "phase" he is on - and hence determine the radial it is on. This in turn allows the pilot to know which way he would have to fly to get TO or FROM the station. So if the detected phase-shift is 180, you must be somewhere "due south" of the station, so flying 360 would take you right to it, while 180 straight from it.
https://en.wikipedia.org/wiki/VHF_omnidirectional_range
The ILS localizer antenna is creating two overlapping beams, one contains a "fly to right!!" code, one a "fly to left!!" code (simplified). If you are straight in the middle, both infos cancel each other out, and you know you are centered on the LOC.
https://en.wikipedia.org/wiki/Instrument_landing_system_localizer
However, you (or the plane) have NO idea which way to fly to stay there! Imagine the runway is 36-18. You are ON the LOC. Unless you know that the LOC is running 360 degrees, you will have a hard time staying on it.
If you know that its APPROXIMATELY north, you can react to the drift in time - so if you fly 355, you will notice it drift to the right, and can correct. But if you start out flying 270 degrees, you will be in the "fly right!!" zone so deep, that you have no idea how far right you need to go, to get it centered again (280? 290? 330?)
You can observe this in the 737. Pick KSEA 34R. Dial 325 into CRS1 and intercept the LOC. The plane will INITIALLY turn to 325, then goes "whoa, this loc is running to the right like crazy, better bank to keep it centered!". Once it tracks it, you will find that its keeping exactly the correct course (to null the drift).
If you have a crosswind (but set the CRS correctly), the effect is the same. Plane turns to inbound course, but notices the "drift" away from the LOC and corrects.
Hope this explains it, Jan