He seems to have thought he was a Christian, at least in terms that would have been acceptable in his day. You might say there's no definitive proof, but claiming there's no proof whatsoever seems to be going too far.
At the very least he was a better public Christian than the current President of the United States, even taking into account the way he murdered his way through his own family.
My claim of "no proof whatsoever" could easily be debunked by a single solitary piece of evidence. I am aware of none. Are you?
I'm assuming you won't accept anything written by Eusebius so I didn't post it. Off the top of my head there's a letter from the emperor to a bishop ordering the construction of a church building in which reference is made to "Our Savior's grace". I realize that's not exactly overwhelming but it's enough to get him killed for being a Christian by a muslim I would imagine.