There is no rule of law (in the common law world ie, UK-based systems) that would render a CVR inadmissible. At it's highest, there might be an argument that because a particular country was a signatory to a treaty, that created a legitimate expectation on the part of an accused that the provisions of the treaty would be reflected in domestic law. That is, however, often not the case and the "stiff s**t" rule has been not infrequently applied.
In most cases, the recording would be made lawfully and with the knowledge of the speakers that what they said would be recorded (even though they had no real choice about it). A court would have a discretion to exclude the evidence if to admit it would be unfair to the accused. Even if the recording were unlawfully made, a court would still have the discretion to admit it into evidence.
The argument would be that the public interest in seeing air safety improved outweighed the public interest in seeing someone tried for manslaughter(s). Whether that would be so would depend on the facts of each case.
In a particularly bad case, involving, for example, multiple deaths, serious departures from procedure, ridiculous speeds and rates of descent and the wilful ignorance of repeated GPWS warnings, a court might conceivably take a view that was adverse to the accused.
I wonder whether the average punter would be terribly unhappy about that? They might think it a bit patronising to be told that because what pilots do is so incredibly cutting-edge, they have protection from the law that isn't available to everyone else.