If Frodo had thrown the Ring in right away

[Celebuial]

After they lost he ring, both Bilbo and Frodo aged quicker. Isn't it likely that Gollum, after having lived on the ring for over 500 years, would age very fast and die within a very short time after the distruction of the ring?

Why didn't I think of that?

Gollum killed the remaining shred of Smeagol when he went back on his promise and attempted to kill Frodo. So instead of helping him it would have completely overthrown him due to the actions he took.

That does make an awfull lot of sense. I never thought to compare Sauron and Gollum in that way. But waht about the part that was left? Would 'Gollum' try to take his life for loss of The Ring or would he continue to sulk around in anguish? I suppose he may not have much time after the destruction of the ring to do anything, but...