It looks like suicide is just mentioned, but it doesn't go into any great detail. So, I don't think it needs it, but if you feel it should have the NSFW warning I doubt anyone would complain. I marked one episode of my series mature for similar reasons, because I prefer to play it safe with stuff like that.
What you could do if you don't want to go as far as marking it mature is just give a warning in the episode title or the description of the previous episode (or even put a sentence at the start of the episode to be sure no one will miss it).