Torbyne |
No, it doesn't look possible to do so.
Overcharge is a unique thing mechanics can do with a standard action.
Shot on the run costs a full action by itself.
You would need two standard actions, a move action and a swift to use both on the same round and even with that, you couldn't make the shot on the run attack overcharged. I don't know of any way to get an extra standard action in a round so until that point it doesn't look doable.