I would not do it....
My childhood house had an avocado and macadamia nut grove in the back. The poultry were also freeranging in the back. As far as I know, there were no issues... BUT, the ground was bare of any weeds and other plant life, while the low avocado branches had leaves that were mostly untouched. I think it was mostly the geese that occasionally nibbled on them.... still, most of them were untouched. So maybe they were allright because they realized to leave them alone.
When my dad brought home a whole bunch of coturnix quail- he wanted me to learn about breeding for profit(apparently the guy regaled him with tales of great profits....) I put them in the aviary, when I noticed the males were harassing the females pretty bad, I wanted to give them shelter to escape the males and to have secure spots for their nests.... cut down whole avocado branches and put them in the aviary. Next day, almost all of the quail were dead, with most of the still living showing neurological symptoms.. only the run that didnt get branches remained alive. It was extremely obvious that avocado leaves was very lethal.
I suppose that is an mixed answer. Free range were fine in the grove, but it was absolutely lethal to those quail for sure. I'd avoid it just to be on the safe side, especially on making it available to confined birds in empty runs with nothing else to nibble on.
