I have no idea about the testicular status of monks, but we can be fairly sure about the Pope.

From the Chronicle of Adam of Usk, written in 1404 and here describing part of the ceremony involved at the coronation of new popes when (in light of fears that a woman might disguise herself as a man in order to be elected pope [see Wikipedia entry on "Pope Joan"]), a suitable precaution was taken...

"...the pope, dismounting from his horse, enters the Lateran for his enthronement. And there he is seated in a chair of porphyry, which is pierced beneath for this purpose - that one of the younger cardinals may make proof of his sex. And then, while a Te Deum is chanted, he is borne to the high altar..."

What fun!