It’s a bit off the clearer attribute of omnipotent, but yes, I’d say God has free will.
And I don’t many, outside some Calvinists, that would say the ability to make free will choices is a necessary attribute of the species we call human beings.
I think it would be part and parcel of self-consciousness and the capacity to act contrary to instinct that separates us from animals.
Can God tell a lie? Can God go against His own perfect and holy nature, and commit sin?