For many reasons, no. First, you yourself produced and distributed the phrase "kill yourself", so you are more likely to be found to be the cause of all subsequent suicides. There are billions of potential plaintiffs who have distributed this phrase, blaming one specific entity take extraordinary evidence. Second and focusing on suicide-specific aspects, an AI has no intent (often a requirement behind laws outlawing "causing" a suicide), which precludes criminal liability, likewise "encouraging" presupposes a mental state that a program does not have.
One might attempt to assign liability for unleashing a "dangerous object", where one can be strictly liable for damages caused by blasting or operating an oil well in downtown Dallas. The hallucinations of an AI do not rise to the level of being ultra-hazardous.
Also note that Open AI does not distribute such pseudo-instructions, whereas SE does distribute user-generated content. The Open AI portal is more similar to a keyboard or computer, it is a tool that one can use to generate text, and it makes it possible to copy and redistribute said text. One cannot sue the manufacturers of typewriters and paper for making it possible to type up and disseminate the text "Kill yourself".
Then also, if Smith used Open AI to generate text that causes death and gets sued, and plaintiff also drags Open AI into court, Smith has to shoulder all of the liability pursuant to the Open AI indemnification clause (§7).