Recent X-ray imaging and analysis, utilizing statistical modeling techniques like Bayesian methods developed for detecting gravitational waves, revealed that one of the mechanism's rings likely had 354 or 355 regularly spaced holes, corresponding to the days in a Greek lunar calendar, suggesting it followed a lunar calendar instead of the Julian solar calendar.These results seem still to be preliminary, but it looks as though the Antikythera mechanism used a calendar more similar to the traditional Jewish one than to the Enochic solar calendar. The traditional ("Hebrew") calendar is "luni-solar"; it has twelve lunar months adding up to 354 days, but adds an intercalary month every two or three years to make up a real year.
There's no indication in the article whether the Antikythera mechanism had any intercalary adjustments. I would guess it did, but given how damaged it is, they probably don't know yet. The Greek lunar calendar had the twelve lunar months, which caused predictable confusion, and it made some clumsy intercalary efforts to make up the difference.
The Enochic solar calendar has twelve months that add up to 364 days per year. That handily keeps the festivals on the same day of the week each year, which prevents halachic difficulties if one were to fall on the Sabbath. But it also gradually departs from the 365.25 cycle of the actual solar year. It is unclear whether the Qumran/Enochic sectarians ever applied an intercalary month to make up the difference.
For PaleoJudaica posts on the Antikythera mechanism, see here and links and (on the Antikythera shipwreck) here.
The answer to my question whether the Enochian astronomers would have approved of the Antikythera mechanism seems to be no.
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