The chests do have a chance to have the ability to be empty as the chests are akin to gambling (even Cayde admits this when he says 'not guaranteeing anything, no refunds').
That being said, if you collect chests/materials in the areas where you have the Cayde's chests; it will put you on collection cool down which also counts for your Cayde's chests.
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No chest in Destiny 1 or 2 has ever had the chance to be empty. I very much doubt Cayde chests are unique in that regard. Further, if that was an option why wouldn't Bungie mention it here? https://www.bungie.net/en/Explore/Detail/News/46359 [i] It is expected that if too many planetary chests are opened within a short amount of time, players may not receive items. Cayde’s Stash and Lost Sector chests should not follow this functionality. We will provide updates on our investigation when available.[/i]
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They also stated later in forum post that it was intentional and that there is a chance for Cayde's chests to be empty. I never stated there was a chance for Destiny 1 chests to be empty, but there WAS a chance for you to be on cool down and receive nothing FROM the chests.
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I’d like to see evidence of that, as you’d expect them to mention that in the investigation post. Seems silly to leave out that fact when looking into that very phenomenon.