Not entirely -- Pummel and Barrage, for instance, already deal basic attacks through an activated non-basic-attack ability.
But the attacks themselves are basic, while farshot is not. You could rewrite far shot to be a basic attack, but then, why not piercing shot? It would be a silly exception.
I believe it would actually nerf Farshot - as it is currently, the ability can bypass One with Nora. By changing it into a basic attack you'd be triggering OwN, thus potentially weakening your farshot champion.
The way Farshot and OwN interact with each other is intended. OwN is supposed to trigger immunities only against basic attacks, otherwise the ability would be much, much, much stronger than it is right now and would most likely go up in its nora cost.