If Smeagol had not died...?

[Gordis]

You are all too optimistic.

I believe Gollum would almost instantly die with the Ring destroyed, turn into dust literally. It was the Ring that kept the 500++ years old hobbit alive.

Note that after the Ring had been destroyed, Bilbo aged very fast:

Arwen: "For you know the power of that thing which is now destroyed; and all that was done by that power is now passing away. But your kinsman possessed this thing longer than you. He is ancient in years now, according to his kind; and he awaits you, for he will not again make any long journey save one."-LOTR, Many partings.

I think it was like that. Bilbo was 50 when he got the Ring. He remained the same age (physically) until 3001, then started to age again. So by 3018 he was 50+17=67 years old physically. With the Ring destroyed, he became 111+17=128 years old all of a sudden, which is very old for a hobbit. Still Bilbo didn't die immediately: the Old Took reached 130 without any magic rings.

As for Gollum, let us say he was 17 in TA 2463, when he got the Ring. He was physically still 17 when he lost it in 2941. He started to age normally, so by 3018 he was 17+77= 94 years old. He was still fit and quite well adapted to the life in the wilderness. In addition there might have been some lingering effects of the ring, making those who had it once age at a slower rate afterwards.
However, Gollum knew that with the Ring destroyed he would die (becoming suddenly 573 years old and thus dead):

And when Precious goes we’ll die, yes, die into the dust.’

And if hypothetically Gollum would have survived the destruction of the Ring, his future would be bleak: madness and misery. Frodo was unable to recover from the shock of seeing the Ring gone, and he had the Ring for only 18 years. What then about Gollum who possessed the evil thing for 500 years? He was better off in the lava of Orodruin, I believe. At least his shrunken tortured soul has found peace.