No the CDX doesn't get pulled locally when you open it or when you amend records.
You can test this by opening a table on the LAN in VFP, then running Sysinternals Process Monitor and filtering to process name = VFP9.EXE and path ends with .CDX.
Then do some seeks and updates and you will see that it is just reading/writing chunks of the CDX on the LAN.
Obviously if you're not taking advantage of Rushmore optimisation it will be doing big, time consuming scans of the DBF instead.