Whether AUC can be calculated as average of sensitivity and specificity or not?
The article you mentioned is referring to the AUC of Receiver Operating Characteristic Curve (ROC-Curve), that is different from the AUC of the Precision-Recall Curve (PR-Curve). See this post to know about the differences between the PR-Curve and the ROC-Curve. If what you want is that same value for the PR-Curve you should look at the F1-Score, see this wikipedia article for an explanation of the relation between the AUC of the ROC-Curve, the Youden Index and the F1-Score. Also a good indicator of the AUC of the PR-Curve is the Average Precision (AP) as explained here.