No, because the cogito guarantees the existence of the subject whenever the subject enacts it. It does not, of course, guarantee the existence of the subject as a continuant.
But there is a catch which helps you. The cogito is not self-standing. Its validity, at least according to Descartes, depends on the existence of a non-deceiving God whose veracity guarantees the truth of our clear and distinct ideas, of which the cogito is one. If Descartes' arguments for the existence of God fail, as is generally agreed, then if there is no God the way to metaphysical nihilism might appear to lie open.
However, whatever metaphysical or theological framework Descartes sets the cogito within, it seems clear that Descartes must exist in order to be able to enact the cogito. This goes against metaphysical nihilism - unless, of course, you do not count Descartes as an 'object' when he enacts the cogito as an (mmaterial) 'subject'.