No, it's quite insufficient.
Unless someone can correct my understanding of the Calvinist position - that it considers man to be totally depraved after being regenerated in Christ due to an inherited sin nature that is a substance pervading his being - then I think it's fair to say that Calvinism is indistinguishable from gnosticism, because they also believed that the body was totally corrupted and thereby unable to do any good. The pre-Augustine church fathers did not believe this, but believed that man had free will to do good. And the fact that Calvinism is essentially the same theology as Augustine's, who was a gnostic for nearly a decade, greatly supports this conclusion.