Yes, in moderation. Raw broccoli (and other brassicas) apparently have mild doses of low-grade toxins. A lot of plants do, it's usually not a big concern. Probably the birds will pick a little and then ignore it. They won't be able to eat much of it anyway, due to the firm nature of the stem.
On the other hand my chickens managed to break into several growing pumpkins... They hollowed them out completely.
My girls really enjoyed my winter garden - broccoli, cauliflower, cabbages. The broccoli did really well this year, and only stopped producing side shoots when the weather started turning warm.
They also ate quite a bit of mustard & collard greens. Now, it's just too hot to grow any greens, so occasionally I'll buy a bunch of mustard greens tie all the stalks together & hang them also. For some reason, they seem to like their veggies hanging up!
With my summer veggies, they've been attacking the soybean plants that I grow for edamame, so I sometimes pull off a few leaves to feed them. They enjoy the cantaloupes that really didn't turn out good enough for us to eat. And any unused tomatoes - but only if they're ripe. The garden is a great place for chicken feed!
Those look like Rhode Island Red pullets you have there....beautiful! I have a couple of reds too. Mine love broccoli! I cut up the stem and all into small pieces and they eat every bit! They like cawliflower and baby carrots too!