Yes. This has been happening for ages and is somewhat common. What's less common but still possible is weapons on the new system that don't have inscription slots.
I'd merch. I don't think anyone would possibly collect such things. People have found Bone Dragon Staves without an inscription slot (quite rare under the new system) but no one is really interested in buying/collecting them.
no inherent mod on a noninscribable weapon is useless as it provides zero bonus...even a 12^50 is a better weapon. As for collectability...who knows. If I were bored and noticed a fair amount of rare skins with no inherent like the BDS or Eternal Blades I've heard of, I'd probably collect them. Maybe someone else already does.