If my logical brain is working correctly this morning, then I'd have to say the answer is "No".
Your printer, **any** printer, will have to be directly connected to a computer in order to work. A router will not be able to tell the printer precisely what to do, it does not hold all the data that a computer does. A computer needs a direct line (be it wired or wireless) to the printer in order to tell the printer what to do.
If I'm missing some boat here, someone please correct me!
If your printer can be used as a network printer (i.e, it has a network card whether wired or wirelss) then yes it will work as well. Most home printers are wireless though and work fairly well when you set it up on your wireless router while a lot of office (heavy duty) printers are wired.