no.
Non molters do, but not true phoenix, only thing special about them is the tail care if you want them to be full and unbroken.
Non molters need a diet free of grains other than brown rice. From what I have read on them, they cant process gluten which is in all forms of grain we have. Over a period of a few years it builds up to a toxic level in their systems and will kill them. They also do well on fish proteins, tons of greens especially lettuce. It has a chemical in it that is great for sustained feather growth.
But again, no for run of the mill normal phoenix, they can eat anything.