If the external enclosure supplies enough power, I don't see a problem. I rather treated myself to the Synology C2 cloud storage. Then created a job in HyperBackup and now live worry-free. The backup is encrypted locally and then uploaded to the C2 Cloud.
You need a DS216+ or DS216+II or higher, the DS216j doesn't recognise the disk, maybe a fireware update will help, but better check with Synology first.