That's certainly what "nation" meant a hundred years ago, and what it means in context of nationalist ideology.
I think that in modern English, "nation" and "nation state" mostly mean "sovereign country or polity". I think this usage is partly because obviously most uses of "state" are references to obviously-non-sovereign internal divisions of territory, whether in the US or Austria or Australia or Brazil or India, and including extremal cases like the states of Palau (most of which comprise less than a thousand people).
Probably another cause is that so few people take 19th-C / 20th-C nationalism seriously that there's no real need for the word "nation" in this context.
But if you're keen on the political-science definitions, note that states don't have to be sovereign. The word "country" won't do because they don't have to be sovereign either (e.g. England or Greenland). I think if you want to formally say "sovereign state", you have to say "sovereign state".