Nope, you only get to ignore the benefits from toughness and recovery powers. So if you hit a character with a stress track like this
OOOO(OO)
with 5 shifts of stress and you satisfy the catch, the target could not use the stress boxes in the brackets and would therefore need to take a consequence. Since the consequence was inflicted satisfying the catch, he can't heal it away with recovery powers either, the consequence would have to heal as if the character didn't have a recovery power.