Gigabit switch on a non-gigabit router?

I have a fairly old router that doesn’t support gigabit. I also have a network switch that does support gigabit. If I connect two devices directly to the switch, then connect the switch up to the router, will the connection between the two devices support gigabit? If I’m understanding correctly the router would just act as DHCP server and give the two devices a local IP address, but the actual connection between them wouldn’t go through the router at all.