Um, no. Reread the rules on stress on p202 of Your Story. They very clearly state that a 2 stress hit fill he second box and only the second box, and so on. If the box in question is filled, you "roll up" and fill the next higher.
This is one of the things that make Toughness strong. With nothing but Good Endurance and Inhuman Toughness someone would need to hit you for 8 stress to go straight to dealing consequences without using your Catch. An 8 stress attack is reduced to 7 by the Armor, filling the 5th stress box and a Mild consequence.