No.

The Jesus = King of Edessa theory is the work of Ralph Ellis, who has no credentials and has written several books about this theory. He also thinks that Paul (as in the New Testament author) and Josephus are the same person. And he also thinks that Jesus is King Arthur.

The claim that Jesus was King of Edessa is based on a curious conflation of kings of Edessa, and distantly related to the tale of Abgar V who wrote a letter to Jesus and received a reply (this story appears in Eusebius’ Historia Ecclesiastica 1.13, and a number of versions of the correspondence floated around).

In Ellis’ made-up version of history, Jesus (Emmanuel) = Izas Manu. This is a fanciful theory with no linguistic grounding based on words sounding vaguely similar. Ellis claims that Izas’ mother was Helena, Queen of the Jews. There is a historical Helena, but she is a Persian who converted to Judaism, not a ‘queen of the Jews’. She is also the mother of Izates bar Monobaz, not Abgar VI.

Abgar Ma’nu VI couldn’t have been crucified and taken down from the cross by Josephus, since Josephus was in Rome at the time, nor did Abgar VI wage war with Rome.

Abgar VII did go to war with Rome, but in the second century. So he is not a contender for this identification.

In short, Ellis work is not historical, his training is not in history, and his theory is speculative nonsense which doesn’t fit basic facts let alone historical plausibility. This is why you never hear him talked about or his theory taken serious.