I have Hawkman JSA, with defense of 15. Adjacent is a friendly JSA figure with a defense of 17.

If I perplex my Hawkman's defense by +1, what will his final defense value be?

17 or 18?

`Le

Well, the effect of perplex last until the end of your turn, so perplexing your own defense is pretty useless.
If you used ICwO, the effect would last until the beginning of your next turn. However, the JSA team ability reads:So, in effect, if you used ICwO to raise Hawkman to a 16, the 16 would be replaced by the friendly JSA member's 17 because the replacement doesn't take effect until just before an attack roll.

Mostly useless, but legal. However, if you were targeting an opposing fig with EE and Hawkman was adjacent to the target, it might be worthwhile.

So to answer the question, Hawkman would have a 17 defense. Perplex can't occur during another action so it would have to be done before the EE attack. However, defense values aren't checked until they are needed so Hawkman's defense value (including the bonus from Perplex) would be replaced by the defense of the friendly adjacent JSA fig.

The +1 defence from ICWO occurs immediately. The defence value is later replaced by the 17 defence from Dr. Fate. Therefore, you no longer benefit from the +1.

In order to get a bonus on top of a replacement value, you need some effect that activates at the same time as the JSA team ability. Energy Shield/Deflection works like that.

Edit: Beaten by Hair10, who added more to the thread besides.