no, my theory is that it is far more socially acceptable and in the public eye in wealthier countries.  It is romanticized in movies and books, celebrities do it etc, so regular folks view it as a viable, romantic idea.
In poorer countries they have a more survivor type attitude, along with deeper religous beliefs that make them not view suicide with anything other than what it is: a morally reprehensible act that goes against the one overriding animal instinct we have: to live.
I think suicide rates actually have very little to do with happiness rates.