We want to speed file transfers between a video-editing system that gets its IP address via DHCP and a file server with a dedicated IP address. Will assigning the video-editing station a static IP address on the same subnet as the file server make any difference in the file transfer speed?

Yes, it may speed up your file transfers significantly if you place the video-editing system (with a static IP address) and the file server on the same IP subnet.

When one IP-connected system knows that another IP-connected system is on the same physical subnet, the network packets are delivered by Ethernet directly to the second system rather than by sending IP packets to the router for forwarding to the final destination.

Once you make the switch by placing both devices on the same physical subnet, try using the tracert command to trace the route to the second system. You should not see a listing for any intermediate stops in the tracert output.

If you still see that packets are going to the router instead of straight to the target machine, change your default router setting to be the IP address of the machine itself, so each PC is its own default router. This should force each machine to check its Address Resolution Protocol cache first, to identify the target machine as local to the subnet so that packets get delivered directly.