When using geoshape as geometry the survey returns an error on submission that it cannot map a Polygon object to a type. (No mapping exists from object type ESRI.ArcGIS.Client.Geometry.Polygon to a known managed provider native type)
Using geotrace and geopoint allows you to submit the survey without issue.
I have modified the geoshape/geotrace example survey from connect and attached which creates the issue for me.
Is there a workaround or am I implementing this wrong? I guess this is related to there not being a default mapping for this question type as documented at Mapping XLSForm questions into ArcGIS Feature Service fields , though it also documents that geotrace is also not implemented which seems to work so I assume has been updated since?