Evidently SCOTUS has ruled on this and it was unanimous.
https://en.wikipedia.org/wiki/Grand_juries_in_the_United_States#Grand_Jury_Clause
Grand jury proceedings are secret. No judge is present; the proceedings are led by a prosecutor;[15] and the defendant has no right to present his case or (in many instances) to be informed of the proceedings at all. While court reporters usually transcribe the proceedings, the records are sealed. The case for such secrecy was unanimously upheld by the Burger Court in Douglas Oil Co. of Cal. v. Petrol Stops Northwest, 441 US 211 (1979).[16][17] The dissenting opinion was joined by Justices Burger and Stewart but concurred with the Court's opinion as to the importance and rationale of grand jury secrecy. Writing for the Court, Justice Powell found that "if preindictment proceedings were made public, many prospective witnesses would be hesitant to come forward voluntarily"; "witnesses who appeared before the grand jury would be less likely to testify fully and frankly"; and "there also would be the risk that those about to be indicted would flee, or would try to influence individual grand jurors". Further, "persons who are accused but exonerated by the grand jury [should] not be held up to public ridicule".[16]