This was done when a Zeppelin tried to run supplies to the forces in German East Africa. IIRC the Zeppelin never made it and disappeared, never to be seen again.
And of course LZ-51 was used in a commando-style rain in the 1971 movie ZEPPELIN with Michael York...
You do not recall correctly.
LZ104 actually flew double the distance it was intended to fly, running the gauntlet of Allied forces in the Mediterranean twice. We do not know what would have happened if the false radio message had never been received or recognized as a fraud, and the rendezvous, landing--and break-up of the airship--had been attempted; conceivably British East African forces would detect and intercept. But the much greater forces in the Med failed to do so, twice!
This ship did meet a final and flaming end in the Med, on a subsequent mission, shot down. It hardly "disappeared!"
The "Afrikaschiff" actually seems to vindicate the concept, as far as it goes.
Actually the air conditions of a trip to Africa and across the North Atlantic are quite different; in some seasons the ocean crossing would be easier and certainly shorter than LZ104's accomplished air-miles. In others--no one in the era of the big rigids ever attempted a winter crossing. Much later, in the late 1950s, the US Navy's LTA program, using blimps that had much more advanced tech but were much smaller, performed "Operation Whole Gale" to demonstrate that by then at least those blimps could survive and operate in those conditions; I don't know if that proves the rigids of the 1920s and '30s could.
On the other hand, certainly the payload capacity of a WWI era Zeppelin, while very impressive compared to the capabilities of even the biggest contemporary airplanes, was tiny compared to any but the smallest of surface vessels. Another thing to consider is that LZ104, as its number indicates, was the 104th hull built by Zeppelin; no rival concern in Germany or elsewhere had built even a fifth as many. The Zeppelin designs evolved quite a lot during the feverish war years. The sorts of ships they had at the beginning of the war were far less capable.
For the Germans to be sending Zeppelins across the Atlantic at the beginning of the war, they'd have had to have started earlier, and a number of advances in materials (such as Duralumin, the aluminum alloy the hull frames were made of) and engines and so on would have had to have been many years more advanced as well.
Then there is the matter of running the British gauntlet. LZ104 certainly evaded it twice in the Med, but eventually on its final mission it was shot down. The bombing raids over Britain also ran into effective defenses. Trying to go around Britain instead of attacking it, they'd probably have better luck, but seaplanes would still be looking for them; if the British were annoyed enough at German success in getting through to the USA they'd probably deploy squadrons based in Newfoundland and the Canadian Maritime provinces as well.
As demonstrations of the commercial possibilities of big rigids in postwar peacetime, these operations would be very salutary I'd think. As war-winning strategies, not so much.