We discuss the transport properties of a disordered two-dimensional electron gas with strong Rashba spin-orbit coupling. We show that in the high-density regime where the Fermi energy overcomes the energy associated with spin-orbit coupling, dc transport is accurately described by a standard Drude's law, due to a nontrivial compensation between the suppression of backscattering and the relativistic correction to the quasiparticle velocity. On the contrary, when the system enters the opposite dominant spin-orbit regime, Drude's paradigm breaks down and the dc conductivity becomes strongly sensitive to the spin-orbit coupling strength, providing a suitable tool to test the entanglement between spin and charge degrees of freedom in these systems.