Personally, I don't think Nick suffered with or had "a mental illness".
He was just pissed off that his records never sold in the numbers that he wished or expected them to. This led to him being disillusioned with what he was trying to achive in life and quite possibly seeing everything out of real life context. John Martyn once said "nice bloke but he had screw loose" which is entirley different to mental illness.
Considering how he became, so withdrawn he disappeared, as someone said, I think we might have to categorize that as something a little beyond "pissed." Unable to talk, unable to face people seems a bit beyond disappointed and grumpy.
I, of course, have no idea if he was mentally ill, but will venture to say that the distance between "screw loose" and mentally ill is probably often hazy and stretchable. At what point does deep depression, or indeed repression, become so pronounced that it can be diagnosed as a disorder?
I have toyed with the idea that he was afflicted with something we'd now call Asbergers (mild autism, those suffering from it are, for example, socially awkward, uncomfortable with touching, making intimacy difficult). But really, this is just my layman, armchair analysis and I wouldn't go so far as to argue the point with anyone, I barely agree with it myself
I do concur with Jason Parker, that to overcome the survival instinct, there is probably some sort if "disorder" involved (I put that in quotes because defining and diagnosing a disorder is subjective - hang on, let me double check my username. Nope, still midnightmoon, not Arthur). But, this point presupposes Drake's suicide, which I'm also undecided on.
On a somewhat unrelated note (although it gives a glimpse into the suicidal mind), I saw an interview with a man who threw himself off the Golden Gate bridge and survived. He said that as his feet left the platform, the first, frantic (and only?) thought that entered his mind was: What have I done, I want to live!