Yes, almost but without encryption. The signatures are blind that means they don't reveal information about the user. For restoring ecash, the client currently asks the mint to re-issue signatures per API.

What we want to build though is even better and also better for privacy, which is simply dumping the mint database publicly so that everyone can download it and restore the ecash locally from it.

It will also come in handy for the proof of liabilities scheme which also needs a db dump.

Generally speaking: the mint doesn't know anything about you so you can safely share its Database with the world (except maybe for metadata things that can be mitigated when implemented correctly).