Nope, it is not.
Its not a Daedric realm under rule of a Daedric Prince.
It only floats in the infinity of Oblivion in the same way that the Mundus does.

Technically, the Soul Cairn is an outer realm.

Yeah, the Soul Cairn is a plane of Oblivion.

Lol.
http://www.imperial-library.info/content/monomyth the http://www.imperial-library.info/content/cosmology.

Yeah, I meant Realm, not Plane

EDIT: A 'Plane' is ruled by a Prince, a Realm isn't necessarily.

EDIT2: Actually, they (Realm and Plane) seem to be used interchangedly? I was just going by UESP's Planes of Oblivion page, but now I don't have a clue

That still only makes it an outer realm, and not a realm of Oblivion, for the same reason that the Mundus is not a realm or plane of Oblivion.

The Aurbis is that section where two infinite spheres touch.
The Mundus with Nirn at its heart is the centre of it all.
It is surrounded by Oblivion, which houses the planes of Oblivion, ruled by their Daedric princes.
Surrounding Oblivion is Aetherius, though that is not quite the correct terminology, but the best one can do when describing nestling infinite spheres.

Anything that is not described above is an outer realm, such as the pocket dimension that housed the Battlespire, the Soul Cairn and the Atronach planes.
They float inside Oblivion, yes, but also in Aetherius and the Aurbis at the same time.

This is a handy http://fc06.deviantart.net/fs71/f/2010/007/0/3/Cosmo_of_Nirn_by_MagusVerus.jpg. The outer realms are not depicted in it, but can easily be imagined as points on the line between Aetherius and Oblivion.

Interesting, thanks.