Not by a long shot. Hulk Hogan still used Real American. Yeah he used the NWO song for a short time in WWE but mostly always used Real American. Steve Austin changed his gimmick to a cowardly heel and never changed his music.
I guess the point is that he is a born again christian rather than an arrogant, self centered bastard but trust me, the only thing that changed was the Christian part. The rest of it was still there.
And I find his "born again" experience to be very amusing. He converted for a girl. As a person who had an actual born again experience, I have found his identifying as a born again Christian to be insulting.