I'm an American who's been living in Germany for the past 8 years. I have also thought about this question, although since I work here, I'm covered under German insurance, so they would probably just put me into a psychiatric hospital, but I don't think the hold would even be that long (Maybe 2-3 days, max?). The cost would all be covered by my insurance.
You could try contacting something like the Deutsche Gesellschaft für Psychologie (German Society for Psychology, dgps.de)- they have an English page, and you can send them an Email in English, and maybe try to ask the question in sort of a round about way ("I have an acquaintance who's traveling in Germany who i'm currently worried about. He's American and mentioned suicide. What would/could happen if he tried it there?" - something maybe like that). Idk, I know that sounds lame, but you could try. Alternatively, you could try the Deutsche Gesellschaft für Soziale Psychiatrie, and try the same thing, and maybe they could give you some further information. Just click on Kontakt, and you can send an Email in English, and will likely get a reply in English.
They may likely send you links to suicide prevention sites, but at least these organizations may be a start. Feel free to PM me if you like. Living here is great.
I just happened across this thread, and if this is true, I don't know if I would consider CTBing in Germany...
https://sanctioned-suicide.net/threads/germans-here-how-to-get-out-of-a-psych-ward.26474/