It would read parity PLUS ALL remaining disks and use the parity calculation to recreate the data for the rebuilt disk.
All New Config does is allow you to assign any disks however you want, and then optionally (and by default) rebuild parity. The rebuild has already assigned the new disk to replace the old disk.
You could make an argument for not having that unused disk in the array at all. Each additional disk is an additional point of failure. If you really wanted to you could go to the trouble to get all the data moved to a single disk, then you could New Config without the unused disk and rebuild parity. But simpler, less trouble, and less likely to cause problems to just keep the disk and keep using it with the data already on it.
Parity always updates in realtime. For the rebuild, there is nothing to update since parity is already correct for the data being rebuilt (that is how the rebuild is able to be correct). It is possible, though, to continue to write to disks in the array during the rebuild, including the one being rebuilt, and parity would be updated for those writes.
Parity check, whether you do it manually or on schedule, is just about checking (and optionally, correcting) parity. But parity is maintained all the time whether a check is done or not.