Yes is is as easy as it sounds, but you will need a switch, not a router. A switch is essentially a traffic cop that directs the network traffic to and from the specific port that a destination computer is plugged into (vs the older hubs, which sends network traffic to all the ports becuase it's not smart enough to know which port the destination computer is plugged into). Switches only care about where the network traffic is going, not its contents, so it won't care if DHCP on the router is turned on or off. Plug it in, turn it on, and you're done.
A router on the other hand requires its own IP address to work on your network which means you'll need to configure the router to play nice with the other router, and routers DO care whether DHCP is turned on in other routers, so it would be overkill for what you're trying to do.
I use a 8 port switch on my wireless router at home with no problem. I use different colored cables for different devices (I.E. red for the printer, blue for the computer, green for the NAS storage, black for the link to the router, etc) so I can tell exactly what cable is going where just by looking.
25+ years in the computer field.