No, it's not possible.
That's the downside of Smart Objects in Photoshop. It allows applying destructive filters without destructing the original, but the pixels of the original can only be edited inside the Smart Object.
The closest you can get is to set up a window with the Smart Object Next to the mother document, edit inside the Smart Object and frequently push Ctrl / Cmd + S to save and update the mother document.
In Affinity Photo there are no Smart Objects, but instead Live Filters. Filters like Blur is just like an Adjustment Layer in Photoshop.
The downside is that it's pretty hardware intensive. In larger and complex documents, I've experienced a latency unlike what I have in Photoshop. So I guess Adobe made Smart Objects like they are because it's unrealistic at the moment for average users to have live filters.
(Edit due to edit in question)
You've added another related question to your original question.
It's possible to make linked duplicates of Smart Objects which share the same content, but can have different effects applied.
Simply Alt + drag a Smart Object and you have a duplicate.
(If you want to make a copy that isn't linked to the original Smart Object, you can right-click it and choose New Smart Object via Copy.)
Having duplicates of Smart Objects doesn't change the fact that the pixels of a Smart Object can only be altered from the inside. Not while viewing the Smart Object in its parent document.