I couldn't say one way or another as to what I think will happen: I know that I would love to see it found, with Tablets intact inside. But I'd much rather see a chunk of St Matthew's Gospel found in a jar somewhere in Jerusalem which would have to be dated to before the Fall of Jerusalem, thus leaving Modernists who deny that Christ predicted that Fall with some egg on their face...

I don't know about the Ark being needed for the Temple to be rebuilt. Maybe there is some Jєωιѕн legend about that with which I am not familiar. The Second Temple, the one known to Jesus Christ, was built without the Ark.

The kinds of Jєωs who would rebuild the Temple to make a point don't believe in literal interpretations of the Bible. They wouldn't believe that the any given box on poles discovered out in the desert was THE Ark. Actually, no one could be sure. Unless a latter day St Helen had the guts to do a little experiment. But would God work a miracle that might aid and comfort those who do not believe in His Son?

I suspect that the kinds of Jєωs who would be looking for THE Ark and rejoice in its discovery are the kinds of Jєωs who might be minded to raze any real attempt at a Third Temple to the ground. In the minds of Orthodox Jєωs, the secularist Zionist is something along the lines of what the Antichrist is in orthodox Christian minds.

I'm not sure that there is really anything that can be called "Catholic prophecy", though lots of Catholics have made lots of prophecies. Just a few points regarding the End Times are considered to be theologically certain, because they are based on Scripture: one point is that the Jєωs will be converted before the end of the world. It would be so nice if this were to be taken as an absolute and not a conditional promise or prophesy.