Thanks Narkissos for saving me a lot of time making the same points.
The initial post made some rather dubious statements about the Essenes and had a rather uncriticial view towards Notovitch and other presumed texts. "Philo for instance recorded presence of Buddhism in Alexandra (Egypt)". Is that the case? Did he refer to "Buddhism" by name? I think the author is thinking of the references to the Therapeutae, which some scholars (imho pretty legitimately) LINK to the Essenes, which then the author (not legitimately imho) LINKS to the Buddhists. A reference to the Therapeutae is very, very different from a reference to a Buddhist circle per se in Alexandria. I don't recall explicit references to "Buddhism in Alexandria" in Philo of Alexandria, but I could be wrong.
Of course, Eastern Buddhism was not unknown to those in Alexandria who were informed on the outside world. Clement of Alexandria in the second century AD, for instance, said that "among the Indians are some who follow the precepts of Buddha (hoi tois Boutta peithomenoi), whom for his extraordinary sanctity they have honored as a god" (Stromateis, 1.15.71). Notice, though, that he is describing followers of Buddha in far-off India....not there in Alexandria.
The initial post mentions very, very late works like the Ikmal-ud-Din which dates to the tenth century AD and which reports local traditions long after the spread of Christianity and Islam through the area. I have no idea about the relevance or veracity of the other "documents," tho the story of Notovitch is well known and his work is better classified as a modern pseudepigraphon than anything else. I personally have witnessed "Jesus in Japan" crackpottery when I visited Japan, complete with fake "ancient documents" to support the claim, so one should be skeptical about claims of a globetrotting Jesus, particularly when the evidence itself is dubious or late.
That does not mean that there could not have been indirect influence, and quite possibly there was .... especially involving the eastern branch of Christianity which had more contact than in the west (see Edward Conze and Elaine Paigels who have argued for some kind of contact between Thomasine gnosticism and Buddhism). But one should bear in mind that influence is often in the other direction; the Lotus Sutra shows a direct dependence on NT gospel passages, some of which can be shown to be later redactions (e.g. a portion of ch. 5 that reflects John 9, which is absent in earlier witnesses to the text, e.g. the translation from Sanskrit into Chinese made by Kumajariva in AD 406).