I recently acquired an old issue of Bird Talk magazine that had an article about wild cockatiels. It said that they LOVE sorghum that's growing in the field when it has a milky head (whatever that means). They love it so much that Australian sunflower growers plant a strip of sorghum at the edge of the field so the tiels will eat the sorghum instead of the sunflower seeds.
On the other hand, the bird-safe plant lists that I've looked at say that sorghum grass and broom corn are toxic. So I'm not sure what's going on - are some parts of the sorghum plant toxic while others are safe, or is sorghum grass different from plain sorghum, or do wild tiels eat something that offsets the toxicity? The Bird Talk article also said that 29 percent of inspected birds had charcoal in their crops, which helps to neutralize toxins.
Long story short: you're probably better off avoiding this stuff unless you can find more information somewhere else.
I hadn't heard of broom corn before but it seems to be another name for sorghum.