If It Doesn't Further the Conflict, Should You Leave It Out?

A writer who attended my retreat/workshop in Tucson recently emailed me with a great question.  It addresses an important choice that writers face every time they work on their books:  what to include and what to omit.

She asked:  "What happens when there is an event or narrative that reflects my theme but doesn't have enough conflict to carry the story forward.  Should I exclude it?"  For example, if a character supported the narrator in her journey, but there was no conflict involved, should this character be part of the book?