I think there are different types of organisation/disorganisation.
One type is being mentally organised, having good time-management, knowing what you have to do and prioritising to get it done.
The other is the physical stuff, tidiness, filing. Ideally you'd have both but I reckon the first is essential and the second is optional (so long as you don't lose pupils' assessments, etc.!)
My HoD (who is very neat and tidy) was talking to me about this, and I commented that she must think I'm ever so disorganised. But her response was that my brain clearly works and I'm "one of those very clever people who is also very messy".
It's true - I always plan ahead, know key dates and deadlines and work towards them. I have ideas to get things sorted so deadlines don't take us by surprise and to make things more efficient. I'm just messy.