Welcome to the Downs, GK Willie!
It's interesting to speculate what an "unpossesed" Gollum would have been like, but I think poor Smeagol was beyond redemption at that point. He apparently wasn't the most admirable of people even before he carried the Ring. After all, he murdered his own kin just at the mere sight of it.
Had Frodo been able to let go of the Ring enough to throw it into the fire himself, I have no doubt that Gollum would have thrown himself in after it, the Ring calling him to his own death as it fell into the pit.
Gollum had owned the Ring longer than anyone, besides Sauron; he was fated to live, and die, with it.
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