Please store the disk safely. The short answer is YES; your data on the drive can probably be extracted. I cannot say how much data may be lost, however. As long as the disk itself is not damaged (armature slamming into the disk due to dropping, for example) and will spin; That is all you need.
Mounting the disk- that is another issue. But data recovery Does not always require mounting the drive. This is true on Windows, Mac and Linux.
This does almost always require the help of a specialist, though and many can be expensive. In order to help you - almost anyone on here would need the disk in hand in order to try data recovery.
On your own, I would recommend you try using Disk Digger (It is what I use at home) and see if it can access the recognized but unmounted drive. The Free Version will not sort your files-- so it can get tedious. You will want to isolate what you want pulled from the drive in the settings before running it. For example, do not search for all image files if your personal photos were all saved in .jpeg format. Just select .jpg, .jpeg when you run the Disk Digger software.
I hope this helps.