Yes, that type of cyclic current draw is a standard feature of most older copiers and laser printers.
The culprit isn't the copy drum, but the fuser assembly. This is a teflon-coated roller that is kept heated by a large quartz-halogen lamp, and used to seal the toner image onto the paper. The lamp is cycled on and off as needed to keep the fuser hot. The lamp can be up to 1000W in size, so it draws a substantial amount of power, which can cause problems for other equipment on the circuit.
Copiers really need a dedicated circuit.
