I dont think so. If your auto-attack lands first, then the skill, yes of course you've gained an attack that would otherwise be -lost- if you didnt. And the reason is because you've used the skill after the auto attack, so timing would be important, yes? But if this option is on, your aa is out of sync with your timing and its burnt/put on cd - and the culprit is the bow! If you weigh the pros and cons, no reason to have it on, and every reason to have it off, no matter how trivial it's, the alternative is always more beneficial, unless your like Illy who uses a Cowbell or Bagpipes instead of the bow, then its largely irrelevant, because he doesnt have a bow.
This would have been sorted out faster if you listened.