Gollum is crazy, we know that, but does he realize that he was once a hobbit who changed? Does he remember any of his former self especially when he meets Bilbo?
Whether he remembers being a hobbit/hobbit-like, he does remember where he came from:
Chapter 5, page 75:
... Gollum brought up memories of ages and ages and ages before, when he lived with his grandmother in a hole in a bank by a river, "Sss, sss, my preciouss," he said. "Sun on the daisies it means, it does."
But these ordinary above ground everyday sort of riddles were tiring for him. Also they reminded him of days when he had been less lonely and sneaky and nasty, and that put him out of temper.
Chapter 5, page 76:
But suddenly Gollum remember thieving from nests long ago, and sitting under the river bank teaching his grandmother, teaching his grandmother to suck -- "Eggses!" he hissed. "Eggses it is!"