I am not an expert on R.S.I. uniform, so hopefully one with more knowledge will answer.
I will state that I have not seen a photo of any R.S.I. soldier wearing such a gorget. Until some pictures can be found, I would stay away from these items.
That being said, Paolo Marzetti in his book Uniformi e distinctive Italian 1933-1945 has a poor B&W picture of such a gorget on p.219. However he offers no discussion of the provenance of the item, just the picture. There are some differences in design between the one above and the one in the book.
The Speciale R.S.I. issue of Uniform e armi (Settembre-Ottobre 2011) doesn't have this gorget. Given the nature of the magazine and that they like to show many of the unusual items/insignia of the units depicted, its omission is telling that such gorgets were not used. They do have a picture of a X MAS gorget on p.90. The construction is different from the German style above and the magazine offers a discussion of its provenance.
Unlike the German Feldgendarmerie, the Carabinieri have many uniform distinctions that indicate their status as military police. Such gorgets were not necessary to identify them.
Given the R.S.I. adopted many German items, it is possible they consider such insignia. However they did mainly stay with using Italian uniform items.
Just my opinion based on limited research.
Pista! Jeff