If the ArcMap Data Frame is set to WGS 1984, and the transformation NAD_1927_To_WGS_1984 _7 (EPSG:1176) is applied, the NAD 1927 and NAD 1983 data aligns within 4 feet depending on the area in Alaska where the data is located.
Patch Available: http://support.esri.com/download/6427