It works, at least for Premium members as described in the page about Solved Mysteries:
Your solutions are gathered in two different ways. First off they are parsed from your cache notes. Secondly they can be found from corrected coordinates on Mystery Caches and Multi-caches. But sadly the Geocaching Live API does not support the retrieval of all your corrected coordinates with one single call and neither can it report which caches you have corrected coordinates for so we can retrieve only those. This is possible for cache notes, so it's only that way we can find all your solutions.