When you delete Object Group (using Delete key, using Delete tool or using group's context menu) Database Designer for MySQL asks you "Do you want to delete all objects in this group".
There are 3 possible answers:
Object Group will be deleted with all diagram objects belong to it.
Object Group will be deleted, but all its diagram objects will stay on diagram detached from group preserving their positions.
Will close this dialog without any changes to diagram objects or Object Groups.
Diagram Objects: Object Groups | Creating an Object Group | Object Group Editor | Adding/Deleting objects to/from Group