This doesn't have anything to do with ArcSDE (which is just the connection and transfer protocols), and has everything to do with how ArcGIS Desktop creates layers.
The Esri st_geometry type supports
st_length() on polygons, and Desktop adds
st_length calls as a matter of habit (I always disable these values, since I nearly exclusively work with WGS84 coordinate systems). There doesn't seem to be a switch within Desktop to check if the layer is ST or PG geometry storage, and choose the appropriate PostGIS function (looks like a bug to me).
You can explicitly add the
st_perimeter(geomcol) functions to a Query Layer at layer creation or by editing the query definition (though if the coordinate system is geographic and the PG type
geometry, casting to
geography would be necessary, e.g.
st_area(geomcol::geography)). You might also be able to specify "st_perimeter(geomcol)" in the column list from Python via ArcPy at map layer creation (haven't tried it, but it may work). I don't know of any way to alter the ArcGIS Desktop default column selection process.