Yes. And they were believers up to the very end. The Russian Orthodox Church has recently canonized them because of this. If staring down the barrel of a gun couldn’t get them to recant, then I have no doubt that they were, indeed, saints.
They’d have been murdered anyway. Their only chance of survival was to have left Russia before they were arrested. I don’t think they would have, even if they had known what would happen. Nicholas had a religious conception of himself as the father of the Russian people.