No it would. Come January 21st, Vance could take over and still be eligible for two full terms of his own.

How so? If someone takes over the office eith less than half the term remaining it doesn't count toward their own two term limitation. If an impeachement happened today or February it would mean the potential difference of that person in office being four years. One term plus the greater than two years, two terms plus to greater less than two years.