The hardcoat surface is very scratch resistant. It can be measured by a Tabor abrasion test called out in MIL Spec 9625. Sealed hardcoat will provide the best dielectric strength. The breakdown voltage of sealed 2 mil hardcoat is about 1200 volts. There is some degradation of the scratch resistance with sealing but it is still very good. Although the thermal conductivity of aluminum oxide is not as good as aluminum (because the coating is so thin) it will have very little impact on the overall thermal conductivity of the part.

I would also recommend the book The Surface Treatment and Finishing of Aluminum and Its Alloys by Wernick and Pinner which addresses the electrical and thermal characteristics of anodized aluminum.