If I have a Gangplank, Naval that is empowered and I conquer Emperor's Dais with it, when the conquer ability of Emperor's Dais attempts to return my Gangplank, Naval, does that trigger the Gangplank, Naval ability to get +3 or does it return to my hand ignoring that?

No — Emperor's Dais returns Gangplank to your hand, and he does not get +3.

The Dais return is a cost within the trigger’s instructions (“pay 1 and return a unit… to play…”), not a choosing/targeting effect on Gangplank, so his Empowered replacement never applies. Even though you select which unit to return, a cost choice isn’t targeting for this purpose (Rule 355.10.c.1; same reasoning as FAQ #12712). You can still pay the cost and make the Sand Soldier.