Constitutionally, it can monitor it.
Whether it is able to understand it is a separate question.
Though, yes it can and has accessed the content of encrypted data, whether because the encryption was broken in advance, or later because it recorded the contents and gained the information necessary to penetrate the encryption later, either through cryptanalysis or by other means of gathering intelligence.
> and in either case can’t meaningfully exclude people in the US from receiving the transmissions, which was supposed to be the rationale for the search.
Yes, there are some methods of getting data into the country for which the government’s ability to mitigate the effects of that are more limited, that is neither a legal nor much of a practical argument against mitigations measures where they are practical.
But that question is relevant, because the utility of any monitoring depends on the subject's ability to evade it. There is negligible value in subjecting innocent people to invasive monitoring if actual criminals have an alternate path to unimpeded communications, because the criminals will disproportionately discontinue using the path subject to monitoring, resulting in a disproportionate cost to innocent people without impeding criminal activity.
> Though, yes it can and has accessed the content of encrypted data, whether because the encryption was broken in advance, or later because it recorded the contents and gained the information necessary to penetrate the encryption later, either through cryptanalysis or by other means of gathering intelligence.
No one has ever demonstrated a practical break of AES.
> Yes, there are some methods of getting data into the country for which the government’s ability to mitigate the effects of that are more limited, that is neither a legal nor much of a practical argument against mitigations measures where they are practical.
It implies that other mitigation methods are useless, because anyone transferring contraband can merely switch to the method not subject to monitoring or censorship, if that wasn't where they started because those methods are more efficient than physical transport to begin with. And if something is easily evaded and therefore useless, surely it can justify no exceptional invasion of privacy.
Physical phenomena are not physical objects.
> And such broadcasts are very much not protected from government monitoring.
The government can't monitor their contents when it's encrypted, and in either case can't meaningfully exclude people in the US from receiving the transmissions, which was supposed to be the rationale for the search.