Without belief there is no faith. Without faith the words are meaningless. Likewise, there is proof enough in history that religion not only survives without government assistance, it will endure even when government is openly hostile. It is our nature to look for the divine. We instinctively seek God.
Government is power.
With humans, that's just the way it is. While it can have great moments, government at its base will always be the struggle for power among self-interested factions. Good systems of government try to check that greed or balance it against itself. Bad systems pretend that's not the case so the tyrant can rule unchecked. Short answer, no.