Can unpowered radio work without ground connection?
If voyager using 20 watts of transmit power can be received from the edge of the solar system, clearly, having any form of earth connection is not vital. Remember that voyager also received an uplink from earth too.

A dipole antenna is balanced and doesn't need an earth connection. A parachutist with a walkie talkie with a monopole antenna doesn't need an earth connection either.

A crystal set uses an undersized monopole because a dipole would be twice the size and need a balanced to unbalanced (balun) converter to work optimally so these are hinderences. A monopole doesn't really need an earth but it does need a local earth plane that the monopole sees as an infinite earth. For a crystal set this "fake" earth plane would need to be about 1 wavelength in radius so, at a frequency of 1 MHz that makes it quite large and conveniently our planet makes life easy for a monopole.

It was the need for simplicity and convenience that pushed the crystal set to require a ground connection.