They do, but those seed pods will ripen, dry out like little paper cups and will scatter the seeds (which will be black by then) in any wind.
It's a good way to self seed a new bluebell wood too
Those stems will pull up cleanly from the bulbs and you can simply shake them over where you want new ones to grow.
They'll need a hard cold before they'll sprout though, but by next spring they'll grow like wee thin onions. The next year they'll be bigger and the next again they'll flower
and just get better thereafter.
Depends on how much light and moisture they get really whether it's two, three or four years to flowering.
They self seed in every nook and cranny in the garden, that's how I know to pull the seed heads; I did them yesterday
and sowed them in a patch of the burnside that neighbours use to dump grass cuttings. I reckon bluebells would look good there
These ones are really the wild hyacinth, our bluebell is the harebell.
cheers,
Toddy