Can quarantine marker be refreshed as an action in Pandemic State of Emergency?
No you can't as the rules specifically state that you place a quarantine market at level 2 as an action. If you where able to upgrade it then it would include that in the rules.

Rules


  As an action, a player may impose a quarantine on the city he is in by
  placing a quarantine marker in that city with its "2" side face up. A player
  may not put a quarantine marker in a city that already has one.