This is an interesting and a serious bug. I am posting it on the Collector session but i have a feeling that ArcGIS Server is responsible for this too.
Steps to Reproduce:
Using ArcGIS Server 10.2.2 & ArcGIS Collector 10.3 on iOS 8.2
SDE Geodatabse on SQLServer 2012.
1-) Publish a Feature Service with (Archiving, Attachments, and Editor Tracking Enabled) with full editing and sync capabilities except the Allow Geometry Updates. (because we don't want our end users to edit the geometries)
2-) Create a Map on ArcGIS Online for Organizations. and enable Offline support.
3-) Download the map to the device.
4-) Make 2 changes -> 1 edit an attribute and 2 add any number of attachments.
5-) The BUG -> The offline map says 1 Update to be synced. You press sync and after some time is comes with an error that the "Sync failed" because "Geometry update not allowed"
6-) The interesting part: All attachemnts are written to the geodatabse expect the edits made to the attributes of feature class itself. And after that the offline map does not show any new UPDATES to be synced.