My answer would be: possibly.
In our non-fictional world, most non-believers would agree that while Jesus was a real person (although it's a disputed fact), he never actually performed any of the miracles described in the Bible. Most early religious texts don't put too much emphasis on the "magic" part and mostly focus on the morals that Jesus was preaching. Now imagine what an actual wizard could do:...
In the Harry Potter world, the following chronology is given of The Prisoner of Azkaban:
Harry Potter wrote part of this essay on the night of 30 July, continuing on into his birthday the following morning. He consulted Bathilda Bagshot's A History of Magic for information on the subject, and incorporated Bagshot's account of wizards resisting burning using the Flame-Freezing Charm and the stories of Wendelin the Weird. After approximately an hour of writing, at which point it was one o'clock in the morning, Harry decided he was too tired to finish the essay and put it and his other supplies away under the loose floorboard in his room. Later that summer, Florean Fortescue, who was knowledable on the subject of medieval witch burning, helped Harry Potter finish this essay when he was lodged in the Leaky Cauldron for a few weeks in August 1993.
If wizards could fake a witch burning, they could probably fake other things to impress the Muggles from the 1st century AD. Many of these tricks could have been later on associated with the stories about Jesus, as the central focusing point of magical stories in the Christian world.
An even easier way to start a religion as a wizard would be to use a False memory charm to instill whatever you wish your followers to believe, combined with a strong Imperius Curse to make them believe. The only real counter-argument I can imagine would claim that The Bible is canon within the HP universe, but there's no mention of that anywhere in the books.
From J. K. Rowling's perspective, it would have been wise to avoid touching the topic at all. Claiming that Jesus was a wizard would infuriate the existing anti-HP Christian crowd. Claiming that he was an actual saint would be problematic from the "interfaith" point of view. Leaving the question untouched is the only logical solution.