No, they don’t. The construction (not constructor, that’s a different thing) script is editor-only. With ordinary Blueprints (no custom C++ base class), the first thing that gets executed is BeginPlay().
Objects pre-placed in a level have their construction scripts ran at cook/“package” time. They are solidified in the level during that process.
Dynamically spawned objects however will run their constructions scripts as they’re created. Events like BeginPlay, where some setup/initialization script can be placed will also be executed at runtime
Interesting. I stand corrected. Maybe that’s something that changed, because I’m reasonably certain that when I started learning UE4 (which was some time ago), they really hammered the point that construction scripts don’t get executed in.