Writing characters = becoming characters?

I wrote recently about how we become totally absorbed in the worlds we create. Do we become such parts of those worlds because we actually become the characters we create who live there.   

Is writing character a little like being an actor?

Both the writer and the actor have to realise that the character is there for a lifetime, not just for the brief time they are on stage or between the pages of a book. They have a back story and a potential future and when we are not reading or writing about them, or showing a theatre audience what they are doing, they still exist and continue to live their lives.

We empathize with our characters and in portraying them correctly, we create empathy in their readers / observers.

In the last couple of days I’ve had to be a father explaining a rather unfathomable divorce to his daughter and I’ve had to be the same daughter not wanting to tell this very father that she has changed and can no longer live with him.

Is it possible that we become even more absorbed in the characters we write about than those that we read about?  Or does the character we’ve created with such care, gain empathy form the reader because of the empathy we’ve employed in creating it? Can our characters actually become rounded and believable unless we put the effort into getting to know them properly?