Hitler himself was very intolerant of any of this mysticism business. All these activities and societies were banned in Germany once they came to power. There was a number of people, in SS mainly, who were deeply into mysticism, and that was tolerated because of their status. So Hitler wouldn't have sent people to search for the Arc, but Himmler & co. might. Just another illustration of a common misconception about nazi-fascist regimes: they are regarded as highly organized, “precise“, bureaucracies, when in fact they were run mostly arbitrary and ad hoc, a consequence of the Fuhrer Principle.