I guess they've changed this in the last 2 years or so because last time I checked they kept your key hostage and only allowed transferring all data, including the key, to a new phone.
There seems to be an issue with recent Android apis that make file access painfully slow that it wasn't able to sync my data in 1 full day. Enabling the "Case Sensitive FS" option on the folder helped a lot.
May I suggest Choqok as desktop client? It handles both GNU social and pump.io (and twitter), and I'm working to implement missing features because it seems we lack client here
GNU social is a fork/continuation* of the StatusNet software (PHP, "OStatus" protocol). pump.io is a similar piece of software (node.js, "Activity Streams" protocol) written by the original StatusNet developers.
*It started life as a fork, but in June 2013 they merged and it became the continuation.