No. It would not.
The +2 damage isn't just competing with the +2 damage from duelling fighting style, it is also competing against the +2 (or more) AC that using the duelling style also allows you to have.
But the weapon you are using is doing -2 damage or more to start with and you are far more limited on your actions and ranged weapons.
You do have a higher AC and that is a benefit to durability no doubt, but that higher AC is competing with being able to use better ranged weapons and have a free hand for a host of things in combat.
Wielding a shield severely limits your combat options. Enemies at long range - you can do nothing unless you have spells, enemies up above on something you need to climb, you need to take a round to unequip your shiled. You grab an enemy that is trying to run away and now your attack options are limited to unarmed strike .... that is the price you pay for higher AC.






