A unification of the Vatican with an Islamic Caliphate would indeed beguile many Christians into a great deception. Perhaps this is what is referred to when scripture says that even the ‘elect’ of God could be deceived by this if permitted?
How many Christians are already being deceived into thinking that Muslims and Christians worship the same God (as Chrislam teaches)?
Islam claims that Jesus will return as the right hand of their Mahdi to conquer the world for Islam (god). A false prophet claiming to be Christ and unite the world’s religions is what many students of prophecy understand is the mechanism for the end-time Beast. Islamic prophecy claims Jesus will return, but denies He is the Son of the Most High.
Biblically ignorant Christians could be easily swayed to follow such a path if Christian leaders like those in the Vatican proclaim such a unification, though from what we know of Islam, it will be an Islamic religion Christians ‘unite’ into.
I believe I remember George W. Bush even making that claim, now that you've mentioned it.