Anodizing does not make the material significantly more resistant to dings and dents, yes a small amount.
Anodizing does resist light scratches and wears a long time. Anodizing is far thinner than a piece of paper, and is only on the surface. It also provides corrosion resistance.
But dings and dents happen because 6061 aluminum is soft and malleable, regardless of the surface layer. Find a chassis made out of 7075 and it will drastically reduce the amount of dings.