Some of the ornamental sunflowers are sold as pollen-sterile seeds. They will not make seeds unless there is another sunflower to pollinate them. Since this hypothetical pollen source would not be Jade, the offspring would not be Jade.
You can see the pollen as a sticky powder on the disc of the sufflower.
If by chance, the Jade plants do make pollen, then they could self-pollinate, and the seedlings would likely include some green sunflowers at least. I do not know the inheritance of the green color, so I don't know what percent of the seedlings wouold be green.
Wild sunflowers are self-incompatible, and the old open-pollinated varieties are self-incompatible. That means they don't accept their own pollen. But the modern inbreds that are used to make hybrids have had that bred out of them. Pollinting your green Jade with an oil or snack type hybrid sunflower would make the next generation produce pollen, and you could then start selecting back to green.
Good luck if you try this.

I am going to try this. It sounds fascinating.