... I question the carbon dating. This level of technical precision was possible possibly 3000 years ago as far as the availability of metalurgical process is concerned, but I posit that it is far more likely that this item is a more recent creation from amongst other similar devices of more recent production.
One key issue is that the majority of the mechanism's larger fragments were brought up from the seabed over a century ago. As far as I know, there was no attempt to map the wreck site at that time, and there was no attention given to describing what (artifact(s)) were found where within the site. In the absence of the sort of stratigraphic mapping / analysis common nowadays, all that can be said is that the fragments came from the site.
Another key issue is specifying which Antikythera wreck artifacts have been subjected to C14 analysis. Even though the collection of mechanism fragments includes pieces of its wooden case, I've never been able to find a clear claim that any of these case fragments has been radiocarbon dated.
I strongly doubt this thing was a once-off creation of some isolated genius ahead of his/her time 2000 years ago. Radio-carbon dating is a valid method, but it isn't infallible. The concretion evident inside the gears of the device could skew the dating.
Depending on (a) which ancient authors' histories one chooses to believe and (b) how one cross-correlates items mentioned among the histories chosen a case can be made for at least a few such devices' existence.
Archimedes is reputed to have built an extraordinary astronomical calculator / simulator, but the few specific descriptions of his device consistently indicate it was a spherical planetarium (of which 2 specimens were allegedly taken from Syracuse by Marcellus).
There are other, far less specific, allusions to the Romans having possessed a pair of similarly sophisticated such devices as of the mid to late 1st century BCE. However, these latter allusions do not correlate with the Syracuse / Archimedes storyline, do not provide enough details about the devices to judge whether they're the same as the purported Archimedes devices or the Antikythera device, and do not clearly correlate with the estimated timeframe for the Antikythera ship's sinking.
Can coral concretion be carbon dated? I think it can.
Yes - coral skeletons / concretions can be subjected to radiocarbon analysis. However, the risks for results being skewed by (e.g.) contamination are increased. Additionally, traditional C14 analysis alone is usually insufficient to determine the age of marine organic materials, because traditional methods based on atmospheric C14 ratios don't account for C14 ratios / levels in the seawater. This problem is typically addressed by conducting an additional form of radioisotopic decay test (e.g., uranium / thorium) as the primary indicator of the organic material's age.