I have two computers connected to an ethernet switch. The switch is connected to my ISP router for internet access, through the switch upstream port (of course). What happens if I unplug the upstream port?

My goal is simple: I want to have a local LAN *without* Internet access, but I still want to be able for my two machines to talk to each other thorough TCP. Is it possible or once I disconnect the upstream port my network is dead? Does it depend on the switch?

I'm buying a cheap 1000 Mbps switch for $15 at Amazon.