The short answer is no.
I mean, this is just silly. There shouldn’t even be a debate.
This is actually not the first time that a Church has had a prominent agnostic or atheist lead a congregation. The head of the Angelican Church (based out of England) admitted that he questions the existence of God and is agnostic. I’m sure groups of atheists would really appreciate it if a hardcore believer in God was leading their meetings.
This very thing was prophesied by Nephi. It’s one of the reasons the Book of Mormon was created for our day, to testify against such gross sins. It’s known as Priestcraft, the use of religion to get rich and powerful using the name of God in vain. I find it interesting that taking the name of God in vain is high up on list of Ten Commandments, right after no other gods before Him and not worshiping graven images. Notice that out of the 10, not many mention the consequences of disobeying them but taking the name of the Lord in vain does: “…for the Lord will not hold him guiltless that taketh his name in vain.”
That really goes for anyone, anywhere of any belief who takes a self-satisfying action using His name for cover. Whether it’s for money or power or violence.
That this sort of thing is even debated shows what a bizarre place we find ourselves as religious people at this point in time. There should be no question – if the leader of a faith cannot be found with a testimony of the basic principle that God exists, then they shouldn’t have that job. They should be removed immediately. If they want to be a lay person in the Church that just warms the bench and contributes tithes then more power to them. But spiritual leaders need to have certain doubts removed before they are in a position of leadership.
The world is in turmoil like never before. Christianity needs to provide a united front against the powers that would enslave men, kill us in the name of their religion and lead societies towards spiritual death. As such Priestcraft undermines core beliefs from within Churches. It should be stamped out like any secret combination. If it ever came out that a General Authority was agnostic, I’d heavily press for them to be removed and I imagine that they would be very quickly.
So good on the United Church of Canada for taking that step. Anyone else who has a leader with a crisis of faith should too and let that person repent and find their testimony outside a position of power.