Can the AUC of the ROC be interpreted as the average recall? The PR curve plots the precision as a function of the recall, and the AUC can be interpreted as the average precision.
The ROC plots the recall as a function of the specificity. Can we interpret the AUC as the average recall?

Not usefully.
It's the recall integrated with equal weight over all possible specificities. That's not typically an average over any well-motivated real or imaginary distribution.
