As far as I can see, the nose cap contacts the outer race of the lower angular contact bearing (as Dan says). This keeps the spindle assembly from falling out of the quill.
The nose cap does not affect bearing preload, in fact there is no way of altering preload on these spindles.
The two angular contact bearings at the lower end of the spindle are placed back to back, (like car wheel bearings) and seperated by two spacers, one seperating the inner races, one seperating the outer races (unlike car wheel bearings which have no spacer for the inner races).
When the nut is tightened at the top end of the spindle assembly, everything comes up hard on its spacers, preload is automatically set.
I am not exactly sure how the preload is achieved. I suspect the spacers are ground to the same length, and the bearings have a slight height difference between inner and outer races. Alternatively, the bearings may have the same height on inner and outer races, and the spacer rings have slightly different lengths (though this second idea doesn't sound right to me). I must check next time I have one apart....
ps, re. leaving out the alignment screw - I can't recommend this idea on a well-kept machine. It seems to me that at least some alignment screws are damaged by the tool holder trying to turn in the spindle. It is important that this never happens, the spindle bore must be kept perfect as possible.