Sigh -- you've opened up a huge can of worms (or, for lack of a better term, just a long discussion).
Daz "props" can come into iClone in a ton of different ways, and sometimes you need to use all the different ways you can to get what you want to work. What you've imported isn't a prop at all, but a figure (you can tell by the bones and the "cloud" part of the structure as it sits in Daz). A figure can be converted into a prop, but then you lose the rigging.
A figure can't have sub-props converted from it. Normally this isn't an issue when it's a real figure, as the example you are showing. You really wouldn't want to dissect that dragon into parts unless you have a very specific thing you are trying to do. So it's not clear to me what your point is here. Where this is usually a big problem is when an actual "thing" comes in as a figure (like a building where the doors are boned to the main structure). In those cases you need to change it into a prop and/or export it in a different manner (and that's where the real long discussion comes in. I'd be glad to actually read someone do that discussion, because for me it's been so much trial and error my head feels like it's going to explode. Just when I think I have a workflow defined I get a figure I cannot debone or otherwise get to the point I need it to be).
So the real question here is, why aren't you taking the dragon and making it into a non-human character? That's the best way to deal with it in iClone, IMHO.
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Mike "ex-genius" Kelley