I can't really see how we could measure that. How do you distinguish between people who are alive because they're just alive and would have been anyway and people who are alive because the AI convinced them not to kill themselves?

I suppose the experiment would be to get a bunch of depressed people split them into two groups and then have one group talk to the AI and the other group not, then see if the suicide rate was statistically different. However I feel it would be difficult to get funding for this.