There is no way, that I'm aware of to attach a GDT to a Note or vs. versus.
You can add the GDT symbols in a note, but you can’t get a frame in it.
But what usually do is RMB a view “Lock view focus” and add my note, then I put a GDT symbol directly below it. Even though the GDT is not attached to the note it is attached to the view itself and will follow that view around where ever it is moved.