Yes, those should be seeds. But I don't know how long it would take. Maureen

Some drumestick alliums are sterile - Even if they set seed, the seed is not necessarily able to germinate. The sterile ones are the hybrid alliums; i.e. crossings between different species.
Amongst the hybrids you will find these Alliums:

Globemaster: Cristophi x Macleanii
Globus: Karataviense x Cristophi
Beau Regard: Cristophi x Macleanii
Gladiator: Aflauntense x Macleanii
Lucy Ball: Macleanii x Aflauntense

The following Alliums are NOT hybrids. They set viable seed:

Allium Giganteum.
"Purple Sensation": special kind of Aflauntense
"Mars", "Mount Everest", "Mont Blanc": All special kind of
Stipitatum

If your drumsticks are fertile, their seedlings will be able to flower after 3-4 years.

Great information! I'm about to buy some alliums and will keep this in mind. Maureen

drumsticks also make a lot of baby bulbs in the ground. In a few years you'll have lots of bulbs.