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}= m_{0}c^{2} + E_{γ}.
But the momentum of the recoiling electron would be p = E_{γ}/c,
leading to a total energy of
[E_{e}]^{2}= [m_{0}c^{2}]^{2} + [pc]^{2}= [m_{0}c^{2}]^{2} + [E_{γ}]^{2}
These two equations are irreconcilably different, because energy and momentum cannot both be conserved..
Bob S
