I tested this myself.
I played Grand Archivist with no minions on the enemy's side, and with two Mind Controls as the only spells in my deck.
At the end of my turn, the symbol on Archivist animated as usual, to indicate that it activates, but then nothing happened. Mind Control was not cast.
Therefore, this actually makes Grand Archivist far better than I thought, because I'm running the card with only Free from Amber and Mind Control. So, if the opponent has no cards on their side, then Free from Amber will always be played. Otherwise if there are minions on the opponent's side, then it's essentially a 50-50 on if Free from Amber or Mind Control is cast.
I also tested that Grand Archivist will not play Mind Control if the only minion that the opponent has is untargetable.