That "should" work. Or, since this a RAID 1 "mirrored" array, you "should" be able to "break" the array and remove the 2nd drive. Make sure the system boots from the remaining single disk. Put the new disk in place of the second disk, copy your drive, then swap drives to put the new in the boot position. Then, no need for enclosure and the 2nd mirrored drive will still have all your old data.
Regardless, you should still make a backup of anything you don't want to lose before starting.
I say "should" for both ways because what "should" work in theory does not always work in the real world - hence, the backup.