How do these usually get checked? I mean, maybe he’s already done this successfully a few times.
They get checked by the lawyer for the other side.
Usually the first thing a Judge's clerk will do before a judge reads a brief is pull all of the authority cited for the judge to have ready-to-review along side the brief itself (if not analyzed, highlighted, summarized, etc. etc. depending on the judge).
Now, whether the judge actually reads them is debatable (I had my doubts sometimes). But you bet your ass that if the Clerk simply cannot find a case, the Judge will be informed of that.
YMMV in State courts, which can be all over the place in terms of professionalism. But you should at least assume your opponent is going to read your cases because the easiest way to beat someone in court is to point out the law you rely on is bad.