For Biblical Unitarians, and from a theoretical standpoint, can God make use of His omnipotence and free will to take on human form and teach us by way of example what it is to live a holy and humble life, from birth to death? According to Biblical Unitarians, is this something possible for God, or is it beyond His capabilities?
My guess is there is no single answer on this for all Biblical Unitarians, but given what I understand of Biblical Unitarianism, the answer is probably:
No. "God is Spirit." (John 4:24) 'Omnipotence' is a word with a classical theological development that isn't found in the Bible, although the word 'pantokrator' which means 'all-ruling' or 'all-mighty' is. God is the Creator (Genesis 1:1). As such, He could create a human who in turn could teach us by way of example what it is to live a holy and humble life - and that is exactly what He did.
"[The incarnation] appears to mean that the divine Maker became one of His own creatures, which is a prima facie contradiction in theological terms. [...] Such an assertion, considered abstractly against the background of Old Testament monotheism, might seem blasphemous or nonsensical— as indeed, orthodox Judaism has always held it to be." Jesus Christ: Incarnated or Created?
"Jesus makes clear reference to two distinct categories in John 3:6 when he says that the “Flesh gives birth to flesh, but the Spirit gives birth to spirit.” Jesus clearly declared God to be “spirit” (John 4:24). Note that he did not say, “I am spirit,” or “God is flesh” or even “The Father is spirit.” By thus placing “God” in the category of “spirit,” when he himself is clearly a man of flesh and blood, Jesus effectively excluded any possibility that he was God. If God, being spirit, can incarnate Himself as a man, then the clear scriptural distinction between flesh and spirit disintegrates. But God the Creator, who is spirit, can create flesh, as He did in Genesis 1."
Athanasius [a bishop of Alexandria who spearheaded what became the orthodox Trinitarian position] says that God can do anything He chooses to do, and that He chose to turn Himself into a man for the sake of our salvation. Jesus Christ is not one of God’s creatures, he insists, but God Himself, incarnated in human form. These sound like clear statements, but, actually, they are hopelessly confused.
Can God do anything He chooses to do? Of course—except those things that are inconsistent with being God. Can He choose to be evil or ignorant? Could He be the Devil—or nothing at all?
Perfection cannot be improved upon or changed. He is not a pantheistic “god” who dwells in everything. He is holy, meaning that He stands apart from and above His creation, yet is intimately involved with it. Therefore, God cannot alter His essential nature, which by definition is perfect, and perfection cannot be improved upon. But even if He could, in doing so He would, by definition, no longer be “God.”
To think God Himself could incarnate is to get caught up in a category error. It is like asking "Could God not be loving?" God is love (1 John 4:8). Or "Could God be unjust?" A core attribute of God is justice. 'Omnipotence' does not mean God can defy his own nature.