Wait no, Boba triggers when you are dealt a face up card from an attack.
Per the preview card, it says "After performing an attack..." so it wouldn't trigger until after the attack phase was completely over.
Integrated Astromech however says "When you are dealt a card" so the moment that face up damage card is dealt, you can eject the astro and discard the damage card. So while Boba still triggers, you no longer have an astromech for him to target.
That means he could get rid of the IA upgrade but that would be pointless so you'd lose Boba for nothing. So if the only upgrades on the X-Wing are a astro and IA, then Boba can't really do much.
