There is no hard drive in printers that I am aware of but some printers do have memory. My Brother laser printer has 32MB of on board memory which is claimed to be able to hold 500 pages. I have also seen printers that have a memory card slot so you can add whatever sized memory card you want.
I just asked Google about printers with hard drives and apparently they do exist. In that case, we would need to know the model number of the printer to determine whether or not it has one. Basically, if it's a desktop model it probably doesn't have a hard drive but if it's an Enterprise model it might.