Paint a Zinc Plated oil Pan?

I don't think your pan is zinc plated. If it were, it would be dull gray.

I've seen this treatment on hood hinges, light assemblies etc. The part is dipped in chemicals that impart a corrosion resistance.

This keeps the part looking new while in stock and is good to combat rusting from moisture inside the pan but I'd paint the exterior for even better corrosion resistance and improved looks.