Sadly, no. The majority of them are doubles because the reproductive parts have become petaloid, thus they are sterile. However, just a few, more semi double than fully so do produce seed and some of them produce double flowered plants. I am waiting on one which is very similar to picture no 1, but the outer parts are all dark green and the inner petals are red. Not flowering yet and the ssseds it produced last year will not flower for a few seasons.
All (except some very expensive new hybrids) Helleborus x orientalis hand their heads, shame really if not in shame!