According to The Right Word at the Right Time (p311):
It is very difficult to use its other than in front of the noun it
refers to; anything else sounds very awkward:
- ?This can't be our dog's bone, but perhaps that bone there is its.
(A question mark preceding a sentence is the usual convention for denoting the sentence that follows as questionable.)
The Cambridge Grammar of the English Language (p471) in its discussion of the genitive its notes:
This form is largely restricted to the constructions where dependent
forms are used.
By dependent forms the CGEL essentially means preceding a noun. That said, the CGEL later lists two examples, only one of which it denotes as ungrammatical (*):
So, the question Is the necklace its? is indeed awkward (or weird), but probably not ungrammatical. But if someone asks me: Whose bone is that? I shall enjoy pointing to my dog and saying: It's its!