I'm running a database server that's under moderately heavy load. I just kicked off xcopy on that box to copy a database backup to a remote server.
I see that xcopy is using almost all my available bandwidth. I'm worried that it will hog bandwidth that the database would otherwise use.
If I lower xcopy's priority in taskmgr, will that de-prioritize the network traffic, or just CPU time?
It will not prioritize network traffic's bandwdith. You will need a third party tool to perform process-based bandwidth throttling. Check out these Stack Exchange threads to find products that you might benefit from:
That affinity is just CPU affinity not network.