You can hatch object with random colors. But if if you want to keep all the entities in your drawing colored 'ByLayer' you will need a separate layer for each color. With this strategy you can create layers with a sequence number, so they stay related and assign a family of colors to them. You can use that family of colors and layers to create hatches with random colors.
Extra information
Tags: polylines, circles, ellipses, splines, color, transition, color, layer, palette, random, solid, sequence, number, letter, roman, increment, add, generate, gradient,