Does unused Blueprint logic cause a performance hit?

Say you have a few full graphs of logic in a character actor that isn’t used, will this cause a performance hit? Is there a “Drag Around” performance hit in some sense or is there only performance hit when events are being called?

If there’s nothing connected it is ignored during compilation, so no.

What if they are connected and accessible during run time but not being called, does that impact performance at all? Or is performance only impacted by events being processed?

The latter. At least as far as the performance of your game is concerned, having that logic connected won’t impact framerate until it is called.

They only impact editor performance and compilation times.