In states where a NOC is filed (NC, for example), does an amendment to the original NOC affect any important dates which might be dependent upon the NOC filing?
First, note that only a small handful of states actually have Notice of Commencement rules on the books. North Carolina is actually not one of those states, but you can find a list of the states with NOCs in this article: What Is a Notice of Commencement? Your Guide with Form Downloads. Each state has differing Notice of Commencement rules, including whether amendments are allowed/accounted for in the statute.
For example, while South Carolina's mechanics lien laws are silent about amending an SC Notice of Commencement, but Florida specifically allows for amendments to Notices of Commencements (at Fla. Stat. § 713.13(5)). In Florida, a Notice of Commencement may be amended to extend the effectiveness of that notice, to correct erroneous information, or to add missing amended information. But, if the Notice of Commencement is amended, a copy of the notice must be directly mailed to (1) any party who has sent a prelim before the new Notice of Commencement is filed, or (2) any party who sends a prelim within 30 days of the new, amended Notice of Commencement filing. That way, anyone who relied on the first Notice of Commencement won't be prejudiced by the new filing.
Ultimately, the answer is: Yes, it's possible that a Notice of Commencement amendment might affect parties on the job. However, on the whole, states do a good job of making sure that parties who have relied on one Notice of Commencement won't be harmed by an amended Notice of Commencement flying under the radar.