Yes, you would be able to connect a "Cable/DSL" router via its ethernet WAN port to a cable from the Network Switch. The router, though, would have to operate in a different Subnet from the main router, i.e. the third octet (number) of its IP address would have to be different from that of the main router to avoid IP addressing conflicts.
Computers in the two different Subnets wouldn't be able to communicate for "File & Printer Sharing".
The alternative would be to connect the second router via one of its LAN ports and disable its DHCP server. It would then behave as a Network Switch and Wireless Access Point, with IP addresses being allocated by the main router.