I have both cancer – in different people, resulting in recovery, remission or death – and mental illness – varying degrees, from high functioning to dysfunctional/realistically a suicide risk – running quite generously in my family. (I've seen it said that poor mental and physical health come together!) My very close loved ones have passed away due to physical or mental illness.
Actually, my mother was very Christian, and the "pray it away" approach to mental illness usually makes me angry, but I really have nothing against the word demons.
I think it's a good word really, to sum up the sheer hell. If you've ever had mental illness, which I have (although I'm mostly societally functioning, at this point but haven't always been), you know you're never free. It's very much like demons or shadows or monsters following you around in your head all the time, terrorising you.
I've also had health issues and although cancer and other issues do relapse and can be hellish and out of control too (and sometimes result in death, as I know all too well), in some ways it's more straightforward. The illness IS a physical thing in the body. It can, of course, torment the mind too, especially in cases of unimaginable physical pain and hopelessness. But that's a knock-on effect.
However, unlike physical illness, mental illness is inseparable from the mind. The illness isn't a zombie or parasite (or well, a demon – I suppose in a way that's what you're getting at?) taking over the person. In this celebrity's case specifically, addiction is not just like a zombie parasite forcing you to move your hand to put the drugs in your body. The illness IS the mind, and hence often (in a way) the whole consciousness/personhood. Matthew Perry and your brother wanted to escape from their own reality so desperately that they were constantly seeking any short and costly reprieve. That's why treatments for addiction aren't just medical, but largely psychological as well.