No. Just out of curiosity, where'd you get that idea? I've never even seen that argued before.
Where do you get your information? No. It was written at least 150 years or more after Christ, and indeed, after all of the other gospels were written. It's a heresy, and it has NEVER been included in the canon of scripture, at any time, ever. It was recognized as "pseudepigrapha" from the get-go, as are about 20 other books from the same time frame. The gospel of Thomas is a Gnostic view (Gnosticism is pure heresy) of the alleged miracles of the childhood of Jesus. It is given credence only by heretics such as the Jesus Seminar and other non-Christian pretender groups. It was not ever given credence by any of the church fathers.
Dictated by Jesus from the cross is what I've heard on the matter.
No.
None of the Gospels were written while Jesus was alive and preaching.
There is one fragmentary letter which is said by some to have been written by Jesus to some followers. The Catholic Church never accepted it as canonical, and even if they had it would have been of no spiritual use, because about all it says is "Greetings, Jonias..." or something about as banal. Jesus was a carpenter by trade, so presumably there were a bunch of tables and stools wandering about Nazareth that he made. Maybe he framed some houses too. None of those things were preserved as holy relics either.
But let's assume, for a moment, that Thomas' Gospel was written during Jesus' lifetime (it wasn't). So what?
No.