You can model and then rig your own figure with DS weightmapping system and give it TriAx rigging and it will be your figure, like Luthbel did with his Cthulhu Rising. It is just as using Poser Setup Room to make figures like Nursoda's figures.

Dawn isn't Genesis morph. It is  a standalone figure which uses (in DS) DS weightmapping/TriAx rigging.

Theoretically, as DS 4.6 now makes TriAx to TriAx autofit process possible, it is totally possible to make autofit clones from Dawn to Genesis/G2F and back. From Dawn to Genesis/G2F is easier because Genesis/G2F already have their own projection templates but from Genesis/G2F to Dawn autofit would require a person who understands autofit well and can make projection templates. But yes, it is possible. With largely more effort even V4/M4 to Dawn autofit is possible.

Transferring morphs from Genesis/V4/G2F might be possible manually via transfer utility but it might be difficult if initial pose for Dawn is much more different than other figures (because it is sort of important in this method). Of course, if Dimention3D would make Dawn-X plugin, it would probably be much more user-friendly to transfer morphs from Genesis to Dawn.