If you check the official definition in the EPSG Geodetic Data Registry, it lists:
Remarks: Used as part of NAD27 to/from WGS 84 transformation for
offshore oil operations - see code 8647. Scope: Accuracy 1 to 2
metres. Used for oil industry operations only. Information Source:
Various oil industry sources.
The transformation parameter values are zeroes, so it's treating NAD 83 and NAD 83 CSRS as equivalent within 1-2 m of accuracy.
Esri has been working on getting permission to redistribute the provincial NTv2 transformation files but we need to deal with each province separately.
Nova Scotia plans to release (not sure if it's available yet) a new NTv2 file but it converts between ATS77 and CSRS 2010.0. This would replace the older NTv2 file which converts between ATS77 and CSRS 1997.0. The paper is online here.
Even if you got either NTv2 version, there's no transformations available between ATS77 and the "original" NAD 83 that I know about.
Disclosure: I work for Esri and am on the subcommittee that maintains the EPSG registry.