The FISA court only handles warrants, not prosecutions. Generally the only parties involved in a warrant request to a court (FISA or any other), are the judge and the government representative(s) seeking the warrant, though the court can pull in third-parties if it wants, e.g. for advice on legal questions.

A secret criminal prosecution trial would be unconstitutional under the Sixth Amendment ("In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial"). Though SCOTUS has unfortunately allowed for some classified material to be kept secret, sometimes (IIRC) even from the defendant and the jury, though usually this is ancillary stuff, not the direct evidence that would secure a conviction.