Yes. And you can depend on this, it's part of the Stacks API, so it's locked down and written in stone. Stack IDs are permanent and guaranteed to be unique within a document. With two exceptions:
If you Cut and then Paste the stack it will be treated as a new copy and may get a new ID.
If you delete a stack then Undo the deletion (so the stack comes back) it will be treated as a new copy and may get a new ID.