Emily, that's how I got my double green-eyed rudbeckias. I had a lot of green eyed ruds one year. Some were Prarie Sun and some were Irish Eyes. My neighbor had double black eyed ruds that year. Apparently a bee carried pollen with that double gene to my yard, and since then my saved seeds have produced doubles with green eyes. I've never seen any like them.
OTOH, some hybrids are sterile- they produce sterile seeds or no seeds at all. I have a few plants like that.
Karen