Agreed!! there were many other 'gospels' that were not included in
the Bible as reason shown below;.
Christian canons
emerged through a complex process in which some books were "chosen"
and others were left out. A tradition of use, authority within the
communities, antiquity or apostolic, and orthodoxy were factors in
deciding which books were "in" and which were "out."
http://gbgm-umc.org/umw/bible/outside.stm
Also, as interesting to read the Gospel of Barnabas, it is more
intriguing to know who the person was.
Barnabas was a Jew born in Cyrus. His name was Joseph and due to
his devotion to the cause of Jesus, the other apostles had given
him the surname of Barnabas; this term is variously translated as
"Son of Consolation" or "Son of Encouragement".
Paul was a Jew who was persecuting the Christians. He is said to
have seen Jesus in a vision and to have become a convert to the
creed of Jesus. Among the disciples of Jesus, Barnabas was a
dynamic evangelist.
Paul also became a preacher, with the difference that Paul began
to over-praise and deify Jesus. "And straightaway he preached
Christ in the synagogues, that he is the son of God." (Acts 9:
20).
ACTS 9:26 and 27: "And when Saul ( Paul ) was come to Jerusalem
he assayed to join himself to the disciples, but they were all
afraid of him and believed not that he was a disciple. "But
Barnabas took him and brought him to the Apostles".
Such was his influence to the first few follower of Jesus
teachings, yet we knew little of him as oppose to Paul.
Back to question asked, should Vatican found the authenticity of
the Gospel is true and endorse it, will Christianity be false?
I doubt that the Vatican will find this gospel authentic because
it goes against the general flow of the Bible. Every
single book in the Bible somehow complements each other and reveals
an overall consistent message, even though the books were written
by different people over different time periods and found in
different locations. That is the beauty of the Bible and perhaps a
miracle in itself :)
So I don't see how this gospel of Barnabas would fit into the
whole thing.