It MAY be a PR disaster, it is not necessarily going to be one. But the possibility exists and that is the primary thing you have to ensure goes right. Bad PR could result in loss of company and, most importantly, reputation in a way that is difficult to recover from, especially when dealing with suicides.
The topic of suicide is quite broad, it very usually is a build-up over time of things that aren't quite right, so instead of trying to - for example - build a hotline for wanna be suiciders, your best option would probably be to build a network of people who may BEFORE it gets to the point where saving a life is necessary. In other words, prevention works better than intervention.
And that's where you could easily make a difference, provided you surrounded yourself of top-notch technicians: by pivoting and providing help at this level, you could get several income streams, for example for cities to fund the project. By ensuring that each website is local but that they are federated into a network, this would also help travellers, so that people from other areas could meet or talk to local people. The design and the privacy concerns are many and varied, so that is part of why you really need to talk to the right people, because they'll know how to minimize/remove those concerns.