No, I don't think that's the case. I have ADHD and 'risk-assessment' thoughts which are nothing but impulses, frequently occur in my mind. Such impulses are never about ending your life-- and mostly about 'what happens if I do X or Y' a sort of intense curiosity.
The more serious thoughts I mentioned earlier began surfacing after 15 years of extreme loneliness, which considerably weakened my mind, then on top of it, another five years of constant struggle against the most vicious stresses one can imagine (no way out, no matter what, but must find a way out). Towards the end of the fifth year of such chronic stress, these suicidal thoughts began occurring.
However, I must also mention that a few years before these thoughts, I also had a serious concussion (unable to walk for months, unable to read, personality change). I'm not sure whether these were due to concussion after-effects but the probability seems low, since there was gap of 3 years between the suicidal thoughts and my concussion.