BL3 cannot get the golden key again after deleting the local archive without enabling cloud archive

If cloud backup is not enabled, the activation code of golden key cannot be used again after deleting the local archive and starting a new game. Does this mean that I will not be able to use these activation codes again?

Golden key codes are redeemable once per platform account. You cannot use the same code multiple times for the same platform+account. This is independent of the status of your local save game folder and cloud backup settings.

And I would strongly recommend that you not delete your save game folder just to start a new game unless you want to start everything completely from scratch with no keys, no bank contents, no Guardian Rank, etc.