What threegardeners described is what I always assumed were the real sugarplums, that is, hard sweets with the color and shape of plums,but the version with marzipan and a blanched almond and soaked in rum would surely satisfy the definition for the adults. Hard to drop that kind in the stocking (or shoe, as the case may be).
And of course, if they were real plums, there could be several choices: mirellen, Indian plums, damson plums, and prune plums plus more, probably. (Prune is the French word for plum, I think.)
It's truly difficult to know. I recently learned that the story Tchaikovsky used was written in Germany many years earlier, so perhaps there WAS overlap between Germans who settled in upstate NY and the German fairy tale that found its way into Tchaikovsky's music.
In any event, you're right, it's hard to reconcile anything actually sweet and fruity with being retrievable from a stocking, intact. Thanks, honeycat, for your thoughtful comment!