This is quite an old "thesis" by Illig originally stemming from a very simple arithmetic misunderstanding. (No: Pope Gregory aligned his calendar to match eastern date as at the time of the Council of Nicaea in 325, not with the original beginning of the Julian calendar)

There is no need for radiocarbon dating to refute it, since a lot of evidence could easily pinpoint it as a crackpot theory, especially:

• Comparison with historical recordings of oriental (esp. Chinese) civilizations.
• Synchronization by well known astronomical events, like Halley comet, eclipses, etc