The grease should be waterproof too. I've seen a pro mechanic use a huge punch and sledge hammer to get an axle out of a VTX 1800. The grease prevents rust and pitting on the axle.
YES! I think my axle and internal spacer had a
different metal reaction; there was a light powdery corrosion. I steel wooled it clean and shiny, and always lightly grease on reassembly.
Always assume water will get into everything, even if it's not supposed to.