No. No. A high-energy photon can collide with a free electron to become a low-energy photon, but it cannot be absorbed. Free electrons cannot absorb photons. This is because they violate energy conservation, momentum conservation, or both.

Here’s a simpler way to understand the concept if you don’t want to do all the complicated calculations. Let’s say that a photon becomes completely absorbed by a stationary electron and its energy becomes kinetic energy. What happens if we shift our frame to the comoving frame of the moving electron? As you can see, a moving electron absorbs photons and becomes stationary. Here’s the problem. The moving electron must have a positive amount energy, i.e. there can be no negative kinetic energy. A photon’s energy must also be positive, regardless of how small (relativity does not allow for a co-moving frame). Two positive values cannot cancel each other, violating the conservation of energy. It is impossible to stop it by having the photon carry the kinetic energy from the free electron away following the collision. This means that the photon is not absorbed in either of the reference frames.