Generally, no. Supplemental actions only penalize the active action for the turn. For example, if someone took a supplemental action to draw their sword and then attacked, you wouldn't penalize their defense, would you?
The only counter example here is a supplemental action followed by full defense. In that case, the full defense provides +2 minus the 1 for supplemental action, netting you only a +1 on your defenses for the round.
At least, that's the way I and my groups have always read the rules.