As written I can't tell if it's setup for that to work. A little more detail such as:
The internet goes the WAN port and one of the 4 LAN ports goes to the switch.
In that setup, it should work.
I have a switch and then a 4 port wireless router plugged into the switch. All the computers are wired into the switch.
Can I plug a network printer into the wireless router and then access the printer via a computer on the switch?