I cannot see any problem with growing strawbs in hangers in the chook pen in fact it is a great space saving attractive idea - might steal it
A bonus is that the bantams won't be able to reach them either
Actually many people including myself have our chooks either living with or foraging in the vegetable and herb gardens or have fruit trees as features in the pens.
Owing to space issues my chook pen is small now but I have many plants in pots and rotate them for the chook yard .These include many greens like parsley and basil and the Asian greens which are easy and fast growing . I always plant more than we can eat and the girls love it when a whole Bok Choy gets thrown in the pen. That would be the favourite apart from geraniums which they destroy so that pot does not go in anymore ! Apparently miniture roses are delicious too !!
They like the chilli bush too.When we had acres the favourite was free roaming pumpkin vines.They never ate it but had the time of their lives playing and hiding in it and I am sure it save the lives of many chicks from hawks etc and a big temptation for the broodies to want to nest under. The first vine self planted but it was such a success we were never without one after that
Go for the strawbs and good luck with the climate these days