Yes.
Its more schizophrenic than that.
I'm glad someone said it. Too much talk about schizophrenia going on here.
You mean dissociative identity disorder (split personalities). There is a difference between schizophrenia and dissociative identity disorder; schizophrenia is basically a split reality, but the personality is still whole; their mind is stuck switching between two worlds or realities. Hallucinations cause the real world to become feared and they retreat to their fantasy world, which becomes even more horrific and goes from a place of solitude to a place of imprisonment. From our world, to Sovengarde; when the disorder becomes stronger, it eventually becomes much like Mehrunes Dagon's and/or Molag Bal's planes while the inhabitants of their Sovengarde becoming the Dremora and Daedroth.
Split personalities; a person experiences only one reality: the real world. The problem is that they're experiencing it through a mind that is fragmented. The main personality suffers amnesia of what went on during the personality/personalities that have split. Akatosh (the main personality) remembers saving the world but not destroying it, while Alduin (his split) would remember saving the world during Oblivion and destroying it.
tl;dr-- Schizophrenia is one person living in two worlds, while split personalities is kind of like two people (in the same body) living in one world. Sorry about the little psychology lesson; I just have a lot of passion about the field ^_^