The Pope's manuscript
Nope. But the next day's NYTimes reported that it was a replica (hence, not actually a manuscript) of a copy of a legal text by Jacob ben Asher. Now I can't find that report, and instead it says it is a replica of a manuscript from circa 1435. (So it probably isn't Vatican Ebr. 151, a Byzantine manuscript from the 14th-15th century with Kitzur Piske ha-Rosh, by R. Jacob ben Asher).
As you may know, a new and comprehensive catalogue of the Hebrew manuscripts in the Vatican libraries is on the way. Meanwhile, I checked the IMHM catalogue and found only two Vatican manuscripts dated 1435. One of them, Rossiana 555, is a copy of Rabbi Jacob ben Asher's major work, the Tur. It was copied in Italy and contains decorations of some sort, making it a likely candidate for the gift (for a short description of the manuscript, see here, at the end of the 'Text' section).
What makes it funny, or maybe upsetting, is that this particular manuscript was copied by Yitshak ben Ovadiah of Forli. Who, according to Nurit Pasternak (Tarbits 68), converted to Christianity.