But do you still draw your normal defense card after that at all?
Can you draw a defense card and then play the armor for additional defense?
Actually, you're required to reveal your defense card first, then you may play Armor if desired. Armor is a Reaction card which is used "while defending". In the Attack Overview on page 16 of the Learn to Play guide and page 4 of the Rules Reference, it details the steps followed when resolving an attack:
1. Declare Defender
2. Roll Dice
3. Reveal Defense
4. Apply "While Defending" Effects
5. Apply "While Attacking" Effects
6. Assess Damage