Here's the info from ASPRS Clifford Mugnier.
Which suggests that Adindan is a bit of a misnomer and it is real the Blue Nile datum.
But there are transforms available in the system.
See
Adindan_To_WGS_1984_4 WKID=1103 Accuracy=6.000
Page 2 and 44 of the geographic_transformations.pdf in the ArcGIS documentation folder.