My gut reaction would be no but single drive -> RAID1 is nowhere near as big a change as a single drive -> RAID0. The NVidia RAID config tool is pretty flexible in what you can do with arrays once the RAID functionality is enabled in the BIOS, I think the latest Intel controllers are possibly even better.
The rest of this is kind of thinking out loud so may be a complete pile of garbage....
The big question however is what happens when you flip the BIOS from normal mode to RAID mode - the current install may or may not (depending on the driver architecture) have the correct drivers to run in RAID mode.
Once RAID mode is enabled you'll need to create an array, the best bet will be to create a single disk array probably as RAID0 with the drive containing the data making sure that you don't select the option to wipe the drive. You'll possibly have to remove the blank disk from the PC to amke sure you get the right one. In theory you should be able to do an online migration from the single disk array to a 2 disk RAID1 array using the RAID utility in Windows.
I think the bottom line is it might be worth a shot but make sure you have a backup of everything and are prepared to do a full reinstall if it fails to work.
