No, it's not. Phonons are not atoms, but collective excitations of atoms. Think of it as waves moving along a string; they can start in one place, and move through the lattice to another place, and keep on going. They're like sound waves in a crystal; in fact, they are sound waves in a crystal. And it's that feature of phonons - that they can move long distances - that sets them apart from the motion of electrons in atoms.
In the classical approximation, the oscillating field of the photon causes an oscillation of the electron, increasing its orbital velocity and leaving it with more energy. We know that's wrong, because orbital energies are observed to be quantised. In QM, we don't know the precise details of the process, but we know the starting conditions and the finishing conditions, and we can deduce rules by which we can work out the finishing conditions from the starting conditions. Again, why should we expect to know any more than that? It's not like we can "see" a photon; photons are the instruments we see with.
Now that's what I call helpful!
Some new questions arise:
1.) Lattice oscillations are produced by .... mechanical energy, say bouncing crystals together like Newton's manager toy? Or are the atoms in the lattice oscillate under influence of .... electromagnetic waves?
2.) If the EM waves excite the atoms in a lattice, producing a propagating wave (which type of wave?), what is the "speed" of the wave? That is, how fast does the wave propagate? Which parameters influence this "speed of the phonon"? Are we able to calculate that speed?
3.) Why "approximation"? Why not exactly measurable? Let's leave that aside - if the electron is oscuillating under photonic influence, what type of oscillation would that be? Oscillations ARE waves. They must have a wavelength. If the wavelength of the photon is known, and the electron is also a wave (is it during transition?), these waves must interfere.
How would you calculate the interference?
4.) It seems FZ uses "phonon" as both lattice vibration and oscillation induced by a photon on the electron. Let's consider that valid for a moment and call it electronic phonon.
5.) You state it is unknown what exactly is going on during the transition. Therefore it must be legitimate to explore this further. This is what FZ claims to do. Maybe he's wrong. But it must be allowed to be questioned.
6.) In mathematics, you can think outside a system. That is what Gödel did, proving that by axioms alone you cannot prove certain sentences from within the system established by the axioms. But by proving that, he transcended the problem, proving, this is valid for ALL formal systems.
Physics is a formal system as well. It developes by expanding the theory to match "reality". But remember, a theory is not an axiom, although it seems to be treated as such.
But certainly a photon will not make you give up!
So lets discuss this, but Dave style please.