In Barovia, the spell fails unless a specific condition is met
All that being said, in Barovia (emphasis mine):
Astral projection, teleport, plane shift, and similar spells cast for the purpose of leaving Barovia simply fail, as do effects that banish a creature to another plane of existence.
... so the banishment spell has no effect until:
Strahd is defeated, [when] the fog that surrounds Barovia fades away, allowing the inhabitants of the valley to leave if they wish.
It is unclear if that event removes the restriction to planar travel or only permits inhabitants to leave through that specific method.
It's unclear for shadow dragons in general
Shadow dragons, according to their Monster Manual entry are:
true dragons that were either born in the Shadowfell or transformed by years spent within its dismal confines
In the former case, their plane of origin would be the Shadowfell, in which case, they would not return, remaining on the Shadowfell. Along a similar vein, a dragon born in most other planes who then was transformed, would also be permanently banished to that different plane.
On the other hand, a dragon born in Barovia who was transformed from some other effect would return (after being banished to a harmless demiplane).
The shadow dragon in Curse of Strahd:
I could not find a reference to one, so it is possible your GM added it to the campaign. If that is the case, it is up to the GM where this specific shadow dragon originated from.
If it is, as you suspect:
... then the dragon's origin plane is still unclear, as no mention of it is found in the module except that:
he had come to the valley years earlier in the guise of a nobleman named Lord Argynvost.
Without any further details of his origin, it will be up to the GM to decide if the dragon is native to Barovia or a different plane.