Is it possible Coach has deluded himself into believing he's performing God's will by voting out Brandon? Possibly. But that doesn't change the fact that he turned on him and is not taking responsibility for doing it or for the fact that most Christians do believe God has given them free will to choose between what's right and wrong--and that it's really hard to see turning on Brandon as being "good" in any way other than that it's good for Coach's game. Speaking of which, the Bible doesn't say a lot that's positive about money, and ultimately what Coach is hoping for is that he'll get a million dollars for manipulating everyone else better than anyone else could.
All through the game, Coach has done any number of things that aren't exactly "Christian" or honorable. He lied about the hidden immunity idol, pretending to find it, and letting Brandon believe God somehow led him to it (and the others who knew about it did the same thing by keeping their mouths shut). He's clearly been intending to use Brandon's loyalty until it became a liability and has said so when out of earshot of Brandon and the others. He used Edna for as long as he could and then cast her aside, even though she was the first (and originally, only) person to be particularly welcoming to him. He also made a big deal of praying in public and forcing others to do so--I still can't forget him yanking Edna to her knees after a challenge where she took a lot of hard hits, because she wasn't quick enough to join his prayer circle of gratitude. I guess Coach missed that section of the scriptures that encourages Christians not to make a great show of their piety.