Are you asking about moving a cache created for a 10.2.2 service to a 10.1 environment or are you simply asking about the desktop client involved with generating the cache. If it's the latter, then I believe you can do this without any compatibility issues if you connect as a Publisher to create the cache. Making an Administrator connection from a 10.2.2 client to a 10.1 server will not work. If it's the former, then I have an opinion to share on that. While I have not personnally tried to do this, I do not see why moving a cache created at 10.2.2 wouldn't behave or publish correctly for a 10.1 service. In looking at the Esri online documentation, the cache tile format and storage format options all have the same possible parameter inputs for both versions of the ArcGIS for Server application. You service properties and input service definition would likely need to be exactly the same in 10.1 as it is in 10.2.2 but I believe theoretically you should be able to move the cache tiles.
