No, your fuel mix does not affect your property's score. Your property is not credited or penalized for the relative efficiency or the fuel mix of your utility provider. While all buildings use electricity, fuel mix comes into play when you consider heating and cooling. Depending on your fuel mix, the technologies within your building used to heat (or cool) will be different, and the use of source energy (in the ENERGY STAR Score) ensures that you do not receive a credit (or penalty) for that fuel type. See this FAQ for more.
However, your fuel mix does affect your greenhouse gas emissions. See this FAQ for more information.