While it is certainly possible that there are vessels from the Second Bais HaMikdash hidden away in the Vatican, I believe it is unlikely.
First of all, the Romans who conqured Jerusalem in 70 were not Christians. If they were Christians, they *might* have kept certain things (such as the menorah, for example) around out of respect for their “parent religion” (especially since, at that point, they considered themselves just another sect of Judaism). But these weren’t Christians – they were pagans. Rome would not be Christianized for another few centuries. It’s difficult to say that the pagan Roman emporers would have kept all this treasure around for centuries without melting it down and using the gold/silver for their own purposes.
Another fact to consider is that Rome has been sacked six times since the destruction of the second Bais HaMikdash.
It was sacked in 410 by the Visigoths
It was sacked again in 455 by the Vandals
It was sacked yet again in 546 by the Goths
And yet again in 846 by Arabs
And again in 1084 by the Normans
And yet again in 1527 by the Holy Roman Empire
I would find it very hard to believe that even if the pagan Romans held on to the gold and silver of the Bais HaMikdash that it would have survived the three barbarian sacks of 410-546 and the latter sackings as well.
Does the Vatican have very old Judaic artifacts? Almost certainly. But I’d be highly skeptical of believing that they have any large major artifacts (such as the aron, menorah, etc.) or anything of any significant size and material value.
The Wolf