Is Writing Real Work?

I've been told by my case manager that I need to find a job. I've been tempted to tell him i have a job: a writer!
I know he'll roll his eyes at me and ask how much it pays.
Most of the people in the shelter who don't have a job just hang around various places, doing nothing. And the person running the shelter says things are going to change.
That got me wondering. Can I truly claim that I'm more productive than those who sit around doing nothing, just because I write blogs, and sit in the cafeteria at night typing away at scripts? Is writing a profession or a hobby? Some might say that depends on whether you get paid or not. I suppose, when you've got no other source of income, that matters.
I am going to try to convince my case manager that what I do, night after night, is better than doing nothing at all, which is what most men in the shelter are doing. And, of course, I am still looking for work during the day, though until I get my ID and a new phone, the number of jobs I apply for will be limited.
So what does the rest of the world think? Does the potential income and definite physical labor of writing beat out sitting around doing nothing? I am worthy to stay in the shelter over the rest of the deadbeats?
You decide!