No, summaries cannot be built with in the way that you've described.
Of course you can have both the Sum and the Avg simultaneously in the measures though.
If you're not interested in having the average appear at the detail level, as it is rather meaningless, you could take advantage of the formatting options to effectively suppress the display of those values, leaving you with only the subtotal level averages. That might be a better presentation for your purposes.
Just go into the Coloring and Limits tab for the Average field and for the detail levels set the Normal values formatting to be white text on a white background.
I know that it's not what you've outlined, but it could be an acceptable solution for you.