If an attacking ship has a defender in its bullseye with an obstruction in between, is the defender still considered in the bullseye for the purposes of certain weapons and upgrades?
Yes. Obstructions don't block the bullseye, they just obstruct the attack if the shortest line (in the attack arc) between the attacker and defender passes through the obstacle. Obstruction usually just gives the target +1 green dice, but sometimes other stuff triggers (like Trick Shot).