Of course we do. Tolkien would never have dreamed I'd get an addiction to chocolate, cigarettes and heavy metal music. I don't worry about being "out of character" at all. As you say, in or out of charecter makes no matter when we're in the wrong universe.
I get the idea of being "historically" AU or canon though. Before I came here, the parts of my life that Tolkien wrote about (however briefly) were very much canon at least to the Silmarillion. I suppose there must be some verions of Maedhros for whom the Silmarillion isn't correct (there are parts in the History of Middle Earth that contradict it).
Either way, canon stops where the published story ends.