GIA offers several different grading products. The ‘diamond dossier’ is generally used for stones below a carat and it includes laser inscription as part of the service so they will all have a number. The tradeoff is that this report doesn’t have a plotting diagram. The ‘diamond quality report’, which is the one generally issued on bigger diamonds offers inscription as an option that is available for an extra fee so some will have it and other won’t. It will depend on what the client requested.
If there is an inscription already present by someone else when GIA examines the stone, they will mention it in the comments section of the report. It’s also possible to have the inscription added after GIA examines the stone, either by GIA or an assortment of other providers. Obviously, this wouldn’t be mentioned on the report.