If they do, there would be a lot of backlash. Both because there's loads of christians in the US, and because Fred Rogers was an icon among many, regardless of religious beliefs or lack thereof. The people making the documentary would be asking for the scorpion's sting if they made Fred Rogers look dumb.
But I have heard that it's preview in a film festival was well received with positive ratings, so that might be an indication that they didn't go that route.
As for how much they would dedicate to explaining Roger's faith, we'll find out when the movie releases nationwide. Considering it was a part of who he was, I imagine some time would be dedicated to it.