Can Rayleigh scattering be thought of as a special case of the Compton scattering?

Compton scattering is scattering of photons off the free electrons. Raylegh scattering is between a photon and an electron bound in an atom, when the photon energy is smaller than the transition energy: $$hbaromega < E_b - E_a = hbaromega_{ba}.$$ Resonant scattering when $$hbaromega = E_b - E_a = hbaromega_{ba}$$ (up to the precision of the level broadening). Finally, Raman scattering is scattering off the electrons bound in atoms when the photon length exceeds the transition energy: $$hbaromega > E_b - E_a = hbaromega_{ba}.$$

The problem with Compton scattering is that one cannot really have a static cloud of electrons - they are repelled by the coulomb forces - which is why one uses weakly bound electrons, which entails a bunch of effects typical for atomic scattering. Yet, Compton and Rayleigh scattering are very different things.

Recoil is another way to look at this difference: Compton scattering involves transfer of energy an momentum between between a photon and an electron, whereas Rayleigh scattering involve tsransfer of momentum (direction of photon changes) but not energy (re-emitted photon has the same energy).