Maybe yes, or maybe not...
If the access LED stays lit up in static green, it could indicate permanent access, e.g. during a copyback/rebuild operation. But in such a situation, the LED(s) of the other disks (at least one in a RAID1) would also be lit. Another possibility could be a disk test currently running.
Could you try and check the status of the controller and the disks attached to it through ServerView RAID?
But most likely IMHO is that the disk is not an original Fujitsu delivered one, and its firmware does not operate too well with the controller.