My very first - second, actually - professional job was doing offline editing, whereby I'd basically make the crash edit/rough cut and the online editor would polish. It embedded in me the same principles I intuitively suspected in music, but never formally studied: tension, sustain, release, transition, context, technical coverage, point of view, rhythm, and narrative. I didn't embark on picture editing as a career, but to this day, almost anything I have done professionally, in interactive media and sound, relies on these principles.
In no way do I think it's necessary, but in my experience, it absolutely helps, primarily in one sense: Building further context around the art of the narrative, linear or interactive, and how emotional reactions can be achieved via media over time. Which is, I'd hazard to guess, what most of us here care the most about at the end of the day.