Do libraries consider adding donated books to their collections?

If I donate a fresh, new, once-read hardcover to the library, does it automatically go into the sell-or-toss bin?

Does anyone note the condition of books in the collection and see that they need replacement? Are donated books considered candidate replacements?

What about books they don’t already own?

If I see that they have four out of five works by a given author in the catalog and I donate the fifth, will they put it on the shelf?

(This question is in Social because I don’t need help, but I’d still like a real answer.)