I have a cheap 100Mbps router that is connected to a switch. I have two computers connected to the switch. The two computers have their IP addresses assigned by the router. If the two computers are communicating locally though, at gigabit throughput, will the data only travel through the switch, or will it also travel through the router and obviously get bottlenecked.
They will communicate directly with one another through the switch if they are in the same subnet. If they are in different subnets, they will have to communicate through the router (which would present a bottleneck). Since they're both on the same DHCP server, they're in the same subnet in this case.
In a general sort of way, communication will traverse as few "hops" as possible to get to its destination. Your switch in this case represents an intelligent device that is capable of directing traffic bound for specific devices bidirectionally, either by MAC address or by IP.
A switch distributes traffic within a network.
A router distributes traffic between networks.
As such, as long as you are only talking within your local network, the clients will never ask their gateway (router), and it will not reach the switch.