I would try it, but only because I'm on the "no shampoo" routine anyway.
I can't imagine it would be any more sticky than say honey, which I've tried.
Also from what I understand brown sugar is also a humectant.
I don't have to try this yet because I don't tend to use things in my hair that leave residue on my scalp. But it doesn't seem harmful.
When I saw this post, I thought you were talking about another scalp exfoliator that was mentioned some years ago which included vodka and Cayenne pepper...
But brown sugar, yeah, I'd try that it wouldn't rip my hair out so....