Of course it all depends on the aircraft you are speaking of. Normally LOC allways captures first and will do so as long as it is within the beam, having said beam think of it as a weaker but wider signal at distance from the ground equiptment. GS capture will occur as the same, just expect more hunting at further distance.
Aircraft are usually set up to adjust gain to finer tolerances as you get closer to the threshold, this is usually done first for the loc on gs cap, sometimes marker beacons trigger stages and RA.
RA input to most autoland systems is not much more than a valid at altitudes but the aircraft w/o it will still fly the ils to the ground, just will not flare in it's absence.
Really any ILS coupled A/P is more or less cat III w/o flare.