The Ahnenerbe went all over the world, pre war seeking out mystic or archaeological stuff. Tibet, Antarctica, Hatra, Damascus, Iraq, Bagdad, etc. Remember, this was pre-war.
The Nazi digging would have found it eventually. And sure, Belloq would have his face fried off- but the Ark would be in nazi hands, not American. Indy got the Ark back into safe hands.