This article on the Blairite think-tank Progress' website seems to suggest they do.
"Laurie Penny, staff writer for One in Four magazine, argues that Gordon Brown should be judged on his record as prime minister, not the state of his mental health"
Wednesday 4.30pm:
Jessica Asato, the acting director of Progress, has sent us the following statement:
"The point of this article by Laurie Penny was to highlight how unhelpful the gossip and rumours surrounding this issue were to the millions of people suffering from mental health problems in this country. On reading the article I’m sure that readers of ConservativeHome will see that this blog post has been taken out of context."