Sure.
Answered in the text when
Gollum is chatting with himself.
--------------
"we'll see. It may well be, O yes, it may well be that when She throws away the bones and the empty garments, we shall find it, we shall get it, the
Precious,
a reward for poor Sméagol who brings nice food. And we’ll save the Precious, as we promised. O yes. And when we’ve got it safe, then She’ll know it, O yes, then we’ll pay Her back,
my precious. Then we’ll pay everyone back!’
Tolkien, J.R.R..
The Lord of the Rings: Vol II: The Two Towers: Book 4: Chapt. 9 -
Shelob's Lair.
-------------
Would she find
the ring? Maybe. Is Gollum taking a decent risk? Probably.
Would she care? I doubt it. Like her parentage, she's only concerned for her own gluttony and has no more use for
Sauron or rings than he has for her (other than as a 'gate guard').
Gollum, like Sauron, misses some finer points in his lust for possession of the Ring, and now the power it may give him as well... which he was totally unfamiliar with when he had it all those years before, by the way. He cared less for its power - only for its ability to let him wrench the necks of some 'squeakeres'. Now, he knows if he has it he can "pay
Shelob back" and "pay everyone back" (including Sauron no doubt, for the horrors visited on him when he was captive.) Of course, he could NOT actually pay them all back, but the power and deception of the ring wants him to believe so, for its own sake.
(Nice recovery, S-eS. 😁)