The short answer to the opening question is: no.
The longer answer is: the RSI had a chaotic organization where different bodies (the State administration, the Fascist Party and the Germans) were a source of power, often in competition. This competition allowed some units to reach a certain degree of autonomy by merely playing one authority against another one, but none reached the independence of the X^ MAS. At best, playing the card of the German support, the Legione Autonoma Mobile Ettore Muti managed to get a certain freedom of action, but without the support of the public opinion gained by Borghese's men. On the opposite side, we could also take into account those bodies of the pre-armistice State which managed to survive under the RSI, often keeping a good autonomy and secret contacts with the Kingdom, such as the Carabinieri and the Guardia di Finanza.