Hi,
Applying NAD_27_TO_WGS_84_conus geotransformation does not get applied if a mobile cache is created. The Mapschema.bin fine has "Not Defined " for the transformation that is needed to go from NAD27 to WGS84 or vice versa. We have seen this issue for a while with ArcGIS 9.X , 10.X as well.
Our research led to some 10 year old post where there is a quote from ESRI product specialist here:
ArcPad only supports three and seven parameter datum transformation methods. Unless you can calculate a local seven parameter transformation for your data, none of the predefined transformations are really that good. The best transformation is the NADCON method which uses two files of shift values to model the differences between NAD27 and NAD83. The files are generally too large to support on hand-helds.