It's not hard to link the Nazis to occult stuff, given that Himmler was a bit obsessed with Norse mythology and even had stuff like the black sun symbol on the floor of the Wewelsburg castle / SS HQ.
To come back to the OP question, Himmler was also obsessed with archaeology to prove the superiority of the Aryan race. Well, Hitler was for it too, but Himmler took the obsession to such extremes that eventually Hitler himself called him out on it.
At any rate, the most prominent archaeological organization was Ahnenerbe (literally, "ancestor inheritance"). Which did send expeditions to such places outside the Reich's borders as Sweden, Bolivia, Tibet and the middle east. They also sent a (failed) commando mission to seize a manuscript by Tacitus from Italy, after Italy surrendered to the Allies.
So, yes, they did send archaeological expeditions all over the place.
Mind you, as you'd expect from ideological fanatics, there was a LOT of pseudo-science and pseudo-history involved. E.g., the expeditions to the middle east tried to prove that the crisis cycle and power struggle in the classic age in the Roman empire were some ancestral struggle between the germanic Romans and the semitic populations in the East. E.g., in Tibet they were less concerned with actual archaeology and more with measuring hundreds of skulls to prove that the aryans in the past were smarter than the other populations there. Etc.
But nevertheless, they did send the expeditions. For questionable science, but they sent them.
They were also fairly obsessed with anything related to judeo-xianity. Mostly the judeo part, but the SS was more fond of norse neo-paganism than of xianity too. They obsessed over such artifacts as the (probably fake, as it resembles a nordic hewing spear more than a greco-roman lance) Holy Lance in the Vienna museum.
IF there had actually been a believable clue to the location of the holy ark, I think it's not too unbelievable that the Nazis could have sent an expedition there too.