Yes. VirtualBox stores a UUID in its disk images. You can backup and restore them. You can even create a new VM on another computer that uses a duplicate. What you can't do is use the original and the copy at the same time (e.g. in two different VMs) on the same computer - VirtualBox's "virtual media manager" will reject the second one you try to use.
If you need to duplicate a virtual disk such that it can be used on a new VM on the same computer, you should duplicate it using the Virtual Media Manager's GUI (or the CLI equivalent.