Two clarification questions: Do you have to run? Do you have to have your hands touching the ground?
If yes to either one, I'd have to say no.
However I would like to point out that using trekking poles on long hikes (with or without heavy packs on your back) allows someone to be more refreshed and comfortable after hiking long distances and hike longer (AKA further) each day. Especially on uneven terrain and on grades.