Broken off drying ornamental allium head- will the seeds ripen?

[faraday]

I was given a 6" across drying allium head with seeds still attached. It looks like a straw coloured star burst! The seeds don't seem ready to drop as in they're a bit green. The broken off stem was dry, brown and hollow. I have it lying on a kitchen bench currently, and am wondering if the seeds will continue to mature to the point where they'll fall off and I can collect them?.