You should use always keep the capacitor because it A) raises the power factor, and B) keeps the ballast from drawing too much current.
But with single 100 or 175W fixture you do not have to worry about power factor, so mains current at all, if there is 1 or 2A current, the minimum wire gauge usable for the mains is rated 6A, so in either case you have plenty of margin.
It become important only when you have many of them on a single circuit, when you are operating close to the maximum wiring load capacity.
Of course, all that is assuming the capacitor is connected directly across the mains input.
When the capacitor is connected "somewhere inside" the ballast winding (mainly the case for multi voltage HX ballasts,...), you have to keep it, because the ballast could be designed so, the 120V line input could handle only the real power, the reactive power is supposed to be handled by way longer winding section (usually the 240 or 277V taps), so it does operate on lower currents.