Almost certainly not how you're thinking, no. When you put a disk into a RAID array (even a JBOD) of some sort you're either using it to create a mirror (which would overwrite the data on the drive with what's already there) or making it part of a stripe set (which... etc).
What you MIGHT be able to do it plug in the drive and tell the RAID controller it's a new partition/LUN and then add a mirror disk to that, which would create a RAID array and preserve the data on the drive. However that requires it to be a system that uses NTFS/FAT32 as it's basic filesystem, and no RAID boxes I know of do that - I'm almost 100% certain the Synology software won't. You could do it with the HP server using a windows OS with a software RAID. You might possibly be able to do it with windows DFS somehow, but I wouldn't begin to tell you how.
Adding a drive into a JBOD array in a way that is non-destructive to the data already on the drive is a pretty unusual requirement.