This question cannot be answered according to the criteria of this site as there is no current Church teaching or Church doctrine that can answer this hypothetical and specific scenario set in the future and at odds with the deposit of faith. And also no one knows what a future Pope will or will not do in a specific situation.
Here is why
Since the question is asking, 'could the Pope then "certify" this person as Christ [come the second time] while speaking ex cathedra?' let's investigate what Popes have said on the second coming of Christ.
Second coming of Christ at the end of time | Pope St. JOHN PAUL II [The Great] | GENERAL AUDIENCE, Wednesday, 22 April 1998
2 This twofold dimension, both present and future, of Christ's coming is apparent in his words. In the eschatological discourse which
immediately precedes the paschal drama, Jesus predicts: "They will see
the Son of Man coming in clouds with great power and glory. And then
he will send out the angels, and gather his elect from the four winds,
from the ends of the earth to the ends of heaven" (Mk 13:26-27).
In apocalyptic language clouds signify a theophany: they indicate
that the second coming of the Son of Man will not take place in the
weakness of flesh, but in divine power. These words of the discourse
suggest the ultimate future that will bring history to an end.
However, in the answer he gives to the high priest during his trial,
Jesus repeats the eschatological prophecy, formulating it in terms of
an imminent event: "I tell you, hereafter you will see the Son of
Man seated at the right hand of Power, and coming on the clouds of
heaven" (Mt 26:64).
Humanity's journey to the Father | Pope St. JOHN PAUL II [The Great] | GENERAL AUDIENCE, Wednesday 26 May 1999
4 Christ's resurrection, ascension and the announcement of his second coming have opened new eschatological horizons. In the Last
Supper discourse, Jesus says: “I go to prepare a place for you. And
when I go and prepare a place for you, I will come again and will take
you to myself, that where I am you may be also” (Jn 14:2-3).
Therefore, St Paul wrote to the Thessalonians: “For the Lord himself
will descend from heaven with a cry of command, with the archangel's
call, and with the sound of the trumpet of God. And the dead in Christ
will rise first; then we who are alive, who are left, shall be caught
up together with them in the clouds to meet the Lord in the air; and
so we shall always be with the Lord” (1 Thes 4:16-17).
We have not been told the date of this final event. We must wait patiently for the risen Jesus, who, when asked by the Apostles
themselves to restore the kingdom of Israel, answered by inviting them
to preach and to bear witness: “It is not for you to know times or
seasons which the Father has fixed by his own authority. But you shall
receive power when the Holy Spirit has come upon you; and you shall be
my witnesses in Jerusalem and in all Judea and Samaria and to the end
of the earth” (Acts 1:7-8).
The fact that the 'Christ' to be certified 'approached the Vatican, met with the Pope, and convinced him that he was the second coming of Christ' is at odds with what Pope St. John Paul II [the Great] quoting Scripture, has said on the second coming of Christ. For example, 'great power,' 'divine power,' 'in glory,' are absent in the scenario.
When the Pope is said to be infallible it is meant he cannot err when ... [please see below] and since the OP forces one to take into account as a fact a scenario at odds with Scripture and Papal teaching and the dogma of Papal Infallibility itself,
- The possibility of making such an ex-cathedra 'certification'(sic) is wrought with problems because other than the Pope's subjective conviction, there aren't any bases in the deposit of faith to make such a declaration.
- The Pope would not be infallible if he were to certify the 'Christ' as Christ come the second time and that contradicts the dogma of Papal infallibility. Subsequent questions would the arise about the Pope himself.
- According to the dogma of Papal infallibility, even if the Pope were convinced, he would not be able to go ahead and make such a certification because he cannot err in such matters.
Hence there isn't a Church teaching or doctrinal answer for such a future scenario i.e. saying this is what the Pope will or will not do because the Church teaching or doctrine says he will do this or that in such a situation. It is also abundantly clear that no one knows what a future Pope will or will not do in such a scenario.1
1. "It should be observed in conclusion that papal infallibility is a personal and incommunicable charisma, which is not shared by any pontifical tribunal." - Explanation of papal infallibility | Infallibility | New Advent.
Additional Note & Passages On the second coming of Christ
The note USCCB note on Matt 24:3 has in part
Coming: this translates the Greek word parousia, which is used in the gospels only here and in Mt 24:27, 37, 39. It designated the
official visit of a ruler to a city or the manifestation of a saving
deity, and it was used by Christians to refer to the final coming of
Jesus in glory, a term first found in the New Testament with that
meaning in 1 Thes 2:19.
Acts 1:10-11 (RSVCE)
10 And while they were gazing into heaven as he went, behold, two men stood by them in white robes, 11 and said, “Men of Galilee, why do
you stand looking into heaven? This Jesus, who was taken up from you
into heaven, will come in the same way as you saw him go into heaven.”
Rev 1:7 (RSVCE)
7 Behold, he is coming with the clouds, and every eye will see him, every one who pierced him; and all tribes of the earth will wail
on account of him. Even so. Amen.
The following is presented for information
It is important to clear up a few things. Ex-Cathedra declarations are all limited to faith and morals as contained in the deposit of faith handed to the Church by the Apostles.
Simply, if it [faith + morals] wasn't with the Apostles and handed down to the Church, and by the Church from one generation to the next, it CANNOT be part of that which can be declared ex-cathedra as infallible teaching.
If the Pope were to sit on the Chair of Saint Peter and declare that Mr. Obama is the President of the United States of America, he would be telling the truth, and apart from doing a silly thing and misusing his office, he would not have made a infallible declaration, because Mr. Obama being or not being the President of United States of America does not belong to the deposit of the faith. The faithful need not believe that to save their souls.
Please note that Popes in the past have venerated the Shroud of Turin, a fact telling of their inner conviction. Yet even in this case, the said Popes have not declared the Shroud of Turin as the burial Shroud of Jesus. Why? It does not belong to the deposit of faith.
The same can be said of Church approved (because not contrary to the faith) private revelations after the death of the last Apostle.
EX CATHEDRA The term commonly applied to the special and explicit
exercise of papal infallibility. When the Pope speaks from the chair
(cathedra) of authority, as visible head of all Christians, his
teaching is not dependent on the consent of the Church and is
irreformable. (Etym. Latin ex cathedra, from the chair.)
Source: Dictionary: EX-CATHEDRA | Catholic Culture
What does the Pope teach infallibly?
For that we go to PENNY CATECHISM 92 and 93
Q 92 Is the Pope infallible?
A 92 The Pope is infallible.
Q 93 What do you mean when you say that the Pope is infallible?
A 93 When I say that the Pope is infallible, I mean that the Pope cannot err when, as Shepherd and Teacher of all Christians, he defines
a doctrine concerning faith or morals, to be held by the whole
Where do those faith and morals come from?
From the Sacred Deposit of the faith = Sacred Scripture + Holy Tradition.
cf. Catechism of the Catholic Church 890 and 891.