I believe there is indeed some dispute as to the letter from Christ (I never heard about it until the just-linked Wikipedia article). King Abgar's letter to Christ seems to have more historical confidence behind it.
Naturaly we may have only opinion about the Apocripha. They could be true. What seems to strange for me is the 'Son of God'
7. And having heard all these things concerning you, I have concluded that one of two things must be true
: either you are God
, and having come down from heaven you do these things, or else you, who does these things, are the Son of God
For the Roman Centurion the 'son of God' was almost natural thing, all the Greek chieftains were gods, the ceasar was god. For a Sirian, religion based on the Sumer-Akkad tradition very close to the monotheism of the Jews An is the God the rest are demiurgi (probably the equivalent of the Angels). They did not believed the 'sons of gods' living among us. The Magi came to worship the King of the Jews, the frankencise to God is later addition.
Imho Eusebius final statement
I have inserted them here in their proper place, translated from the Syriac literally, and I hope to good purpose.
is more refutal of the Thomas tradition than acknoledgement of the authenticity. I may be wrong.