Bob S

Err......no.
For simplicity, let's consider the total absorption of a photon by an electron in the lab frame, where the electron is initially at rest. For a photon of energy E_γ = pc and momentum p = E_γ/c , the final total energy of the recoiling electron would be

E_e= m₀c² + E_γ.

But the momentum of the recoiling electron would be p = E_γ/c,

leading to a total energy of

[E_e]²= [m₀c²]² + [pc]²= [m₀c²]² + [E_γ]²

These two equations are irreconcilably different, because energy and momentum cannot both be conserved..

Bob S