As the investigation was ended because Mr Murat couldn't be arguido any longer, the McCanns likely would have been granted an "inquiry" (instrucção) had they required it (it was their right as arguidos). It is the magistrate hierarchically superior to the magistrate who decided to shelve the case who accepts or rejects such a request. The inquiry is directed by a special judge. He is the one who decides which interventions must be performed. There's always an oral and contradictory debate in which participate the Ministério Público, the arguidos and their lawyers. After that the judge decides whether charges are enough or not for Court.
I'm not sure but it seems that if the McCanns had made that option, their arguido status wouldn't have been lifted. It seems likely that the Inquiry Judge would have first required the reconstruction of events since the boosting of the investigation needed it. But they would have had some rights, as they had rights in the investigation, being arguidos, though they didn't use them. The main right was to require specific interventions related to the disappearance of Madeleine.