I would say yes as now connected to your network through the router.
I do this with a wireless all in one.
Put the supplied printer/scanner cd in the computer and ready to go.
Not sure about smartphones as would need the driver and scanner software so only compiuters i would think but might be proven wrong.
Have you bought the printer, what does manual say or if not can you get this off the manufacturers web site on the printer web page, what does it say.
Me just going on what my wireless one does. Needs the cd installed on computers so phones it wont do. not sure about ethernet connected ones. sounds posh, normally usb to single computer or wireless like mine, (can do both, no ethernet network conection).