If it's a modem-router then yes you can use the old modem as a router/switch, but you will need to disable a few things though.
Since you are using another router to connect to the net you don't want to have 2 DHCP servers running on your network so disable DHCP on the modem.
You will also have to assign it an IP address manually.
You should also disable any router related services like NAT, Firewall etc. all of that is taken care of by your main router.
Other than that you should be fine.