Kind of... Yes, in that the npub locked tokens can only be redeemed at the Mint by the person with the nsec. I posted a locked token a while back:
https://primal.net/e/nevent1qvzqqqqqqypzpnkq73xs6exkm8t6rjzvxv84gel82txgkpjlwg8gwjsta5w9g9kjqyt8wumn8ghj7etyv4hzumn0wd68ytnvv9hxgtcppemhxue69uhkummn9ekx7mp0qqszkeuys4ulvpk9cemjpplnkyqvsxd3q99262medk7ktlqkpjm4l4gjrjwkn
No, in that the Mint is the one who checks the unlock signature is valid. You could be rugged by a Mint if it is untrustworthy or disappears.
So it's kind of a joint custody... you and your Mint.
