In this work we study the pressure-dependent phase diagram of polyethylene (H₂C)_x from 50 to 200 GPa. Low-symmetry, organic polymeric phases, that are dynamically stable and thermodynamically competitive with elemental decomposition, are reported. Electronic structure calculations reveal that the band gap of the lowest energy polymeric phase decreases from 5.5 to 4.5 eV in the 50-200 GPa range, but metalization occurs only for pressures well above 500 GPa. The possibility of metalization via doping was also investigated, observing that it can be achieved through boron substitution at carbon sites. We report a sizable electron-phonon coupling (λ ≅ 0.79) in this metallic phase, with an estimated superconducting transition temperature of about 35 K. However, a rather narrow domain of stability is found; most of the dopant elements render the polymeric phases unstable and induce amorphization. This suggests that doping under pressure, though presenting an alternative route to find high temperature superconductors, would be challenging to achieve experimentally.