Answer
For the majority of cases, connection files created at 10.1 will be usable at previous releases of ArcGIS Desktop. Only connection files created at 10.1 in the following three ways cannot be used at previous releases of ArcGIS Desktop:
1. Database Authentication is being used and the user name and password are being saved with the connection file.
2. Connection syntax is not supported at previous ArcGIS releases, such as Oracle Easy Connect syntax or when IBM DSN-less connection strings are being used in the instance parameter.
3. The connection is being made to an enterprise geodatabase at a version that is not supported by the release with which it is intended to be used.