There was a point where I'd have taken the option if it was available, so I'd have been supporting the statistic of it increasing the attempts, I wouldn't have met the age criteria for the question though.
In order for it to not increase suicide attempts (to a statistically significant amount at least), I'd first say the age threshold would have to be raised quite a bit more to around 27+. I don't have much more faith in the mindset of a 20 year old than I do a teenager, still too naive in general at this point.
Though I say this without entirely thinking through what life would be like if everybody got such a button, and therefore some time to reflect and adjust to it after the initial darwinian demonstrations around them given them a better idea of its true potential.