I would think only if you linked it to egoistic suicide. But I find it an interesting question, even though it isn't my area of expertise, because in the 19th century the mentally ill were often referred to generically as "the alienated" and the psychiatrist as the "alienist." Thus, it would make sense that the alienated might feature a high suicide rate. I love the articulation of the alienation concept in Os Guinness' Dust of Death, in which he talks about 4 dimensions of alienation: theological, sociological, psychological, ecological. Thus, we can be alienated from God, others, ourselves, and the environment.
Yes, it can,via Marx's multi-dimensional concept of alienation (Verfremdung) which includes all these forms of alienation and is also referred to as I recall by Emile Durkheim.