Yes, but it can only be used as long as it hasn’t been spent already. A user can validate it offline to prove that it has been signed, but that signature isn’t invalidated when it’s spent. The mint stores whether a reference has been spent or not.

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That's the case with normal ecash that you hold for later spending.

You can request ecash from the mint that you cannot spend because you can ask them to lock it to a certain public key whose private key you don't know. You have to give that locked ecash to someone with that private key so that they can spend it. The mint will only accept it from them.