The answer is a simple one. No. Never. Not on your life.
The RC Church is not a democracy and frankly doesn't give a tuppenny damn what its adherents think. It sees the pope as only answerable to God - not cardinals, not bishops, not priests and certainly ordinary people that include those sub-humans 'women'.
There have been popes in the past who have raped (eg, Alexander VI), murdered (ditto), committed incest (ditto), committed what even by the contemporary standards were war crimes (ditto), and they survived - well he did until he was apparently poisoned by his bast*rd son Cesare Borgia, the athiest former cardinal, mass murderer and rapist who raped his sister and murdered his brother, obviously inspired by the morals of his father, the Pope.
The Vatican isn't concerned about tomorrow's headlines. It thinks in terms of the next hundred years. Even when Popes Paul VI and John Paul II wanted to resign due to ill-health they dared not for fear of the implications of setting a precedent for successors. So Benedict will not be resigning no matter what the reaction is to revelations about him. The Vatican's lack of concern was shown in the fact that the only bishop to actually come out of the Dublin archdiocese investigation into the handling of abuse cases, Archbishop Martin, was silenced and Bishop Drennan allowed to dodge resigning. The Vatican doesn't give a fig in reality what people think. It never has. It just does what it wants regardless.
(A classic example was in the 19th century when the widespread human rights abuses, and imprisoning of Jews in ghettos in Rome and the Papal States, was condemned the world over. Yet every complaint was met with the response that it was none of the secular world's business how His Holiness ran the Patrimony of St Peter - as the Papal States's official title was.)