I believe Gollum's life would have ended very soon after the destruction of the Ring anyways. Remember, Bilbo was already nearly sleeping away, and he was "only" 130 years old - compare it to Gollum, who was over 500 years old. He wouldn't have lived long enough to get into Valinor, I think.
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"Out of doubt, out of dark to the day's rising I came singing in the sun, sword unsheathing. To hope's end I rode and to heart's breaking: Now for wrath, now for ruin and a red nightfall!"
~Eomer
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