Depends. In my experience, it usually does exist. Now there are hallucinations where GPT makes up stuff or just misinterprets what it read. But it's super easy to read the GPT output, look at the cited work, skim works for relevance, then tweak the wording and citing to match.

If you just copy/paste and take GPT's word for it without the minimal amount of checking, you're digging your own grave.

the thing they are citing actually exists

In case of RAGs it exists in searched dataset.

and if it does exist, contains the information it claims.

Not guaranteed.