Not accurate. Among many problems, when electrons move, they do tend to move near the speed of light. (The low rest mass means that even tiny amounts of kinetic energy really get them zooming along.) However in Ohmic conductors they frequently crash into scatterers, bouncing off at a random angle and imparting heat to the material. In everyday materials like copper at room temperature, they spend so much time bouncing around that the average velocity of a conduction electron is low.

EDIT: If you want to teach electricity, describe it as a fluid acted on by fast-moving pressure waves. Resistance can be reasonably described by analogy to a viscous fluid flowing through a sponge.