Creativity and the ability to focus exclusively on one activity are different subjects that can or cannot be together and one doesn't imply the other.
You can be very creative, as in my case, and do many things almost at the same time, you work on some task and solve the problems of other task.
I said "almost" because the theory tells that man can handle one thing at the same time and woman can do two at the same time.
This is the theory, don't know if is true or not, I can do only one thing, but I can switch tasks very quickly.
A creative process you can divide in two parts:

• The creation itself that is a mental process that depend on imagination, inspiration and insight. Is here where all is created, you do nothing, only think and create.
• The second part is executing the creation that already exist in your mind, it's a mechanical process and it can be even something automatic and so, your mind is free to do other thing as another creation or do nothing.
  For example, you create some scene, once the scene or the sketch exist in your mind, you open Poser, begin to load the figures, props, pick textures, move your mouse. This is something mechanic that doesn't require too much your attention, so your mind is free to do other things, hear music, think or do nothing.
  Time to time you have to give attention to what you are doing, many times the result is not what you had in your mind and have to break your head how to do it, other time you need some prop that you haven't in your library. You have to interrupt all what you are doing, search in your DVDs, in the internet or even purchase what you needed and then return to your work.
  The two parts of the creative process not always are separated, many times can be mixed or iterative, you started with nothing in your mind and ended with something or you started with some thing and the final result was something different and not always related.

As for addiction and obsession I have no idea.

Stupidity also evolves!