No. Federal law prohibits the NTSB from releasing any CVR recordings, and the NTSB notes that they are exempt from FOIA requests. The same law requires them to release a transcript, like the ones seen in accident reports, if the transcript is relevant to the accident or incident.
See 49 U.S.C. § 1114(c):
(1) The Board may not disclose publicly any part of a cockpit voice or video recorder recording or transcript of oral communications by and between flight crew members and ground stations related to an accident or incident investigated by the Board. However, the Board shall make public any part of a transcript or any written depiction of visual information the Board decides is relevant to the accident or incident—
(A) if the Board holds a public hearing on the accident or incident, at the time of the hearing; or
(B) if the Board does not hold a public hearing, at the time a majority of the other factual reports on the accident or incident are placed in the public docket.