No, there are no parentless Christmas Stars. They are not found in the garden. They are ONLY obtained by breeding a Christmas tree with a Poinsettia.
If you're asking can you get a Christmas TREE seed from the garden, yes, you can. There are at least two variants of Christmas trees that can only be obtained via breeding (a Christmas tree with a Christmas tree), but the other five variants I think can all be obtained from the wild. There are several variants of the Christmas tree that look almost identical, so be careful before giving any away on the donation thread. If you have two that look the same, and you check the compendium and it appears that the same one is there twice, that means that the two you have are NOT identical. It's easy to be fooled; you have to magnify the page quite a bit to see the difference, really.
Btw, the breeding period for Christmas Stars is not always exactly the same as the breeding period for Christmas Trees. The admins will announce the times to everyone. Usually Christmas Stars come a little after the trees, so newcomers have a chance to raise a few Christmas trees first.