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.

Yes, it is possible. Many antenna types are self-contained, in that they don't require a ground or use ground as one of the two connections where the signal appears between. Dipoles, folded dipoles, and loops are just three examples of such antennas.

The reason most crystal radios work with a long line antenna and the other connection ground is because that's a good way to intercept reasonably high RF power, relatively speaking. A dipole the full length of a blimp and hung below it might intercept enough RF power so that you can hear the demodulated signal with the right headphones. The orientation of the blimp would be important. It would pick up signals to the sides, but not directly in front or in back. There are other self-contained antennas that have other radiation patterns, but their shapes wouldn't be as compatible with the stucture of a blimp.

Polarization also matters. One problem with the blimp dipole is that it would pick up horizontally polarized transmissions. Most commercial AM, for example, are vertically polarized.

Of course the available power in the air is important too. Being close to a powerful transmitter helps a lot.

Back in grade school, I had a long line antenna out a window in my room to a shed in the back yard, maybe 60 feet long. I could pick up a 50 kW AM station from about 20 miles away reasonably well with a crystal radio and the right headphones. The orientation of the antenna was about right for the direction to the transmitter, but the polarization was opposite. There was apparently enough scatter and diffraction so that it still worked.

I recall that early crystal radios sometimes used wide loop antennas (like a hula hoop, or a several-feet square diamond, or octagon. Or basket-weave coils many inches in diameter.) Look up: crystal radio loop antenna.

https://www.google.com/search?q=%22crystal+radio%22+loop+antenna+diamond&source=lnms&tbm=isch&sa=X

In early internet days some guy had a ferrite antenna, using a collection of inch-thick ferrite rods, in series segments totalling several feet long! (Also, I see a reference to "ferrite sleeve" antennas, so that might be another possibility.)

Hobbyist VLF antennas aren't possible? Since they're fifty miles wide? Nah, just build a tuned, short antenna, where the Electrical Aperture EA is far, far wider than the physical parts. Those antennas act as "wave-funnels," where they may be electrically a quarter-wave wide, even though they're physically only .0001-wave in width. Essentially, if you build any large VLF radio antenna project, it can also be tuned for AM band. Look for DIY groups doing "natural radio" or "diy vlf antenna," or perhaps "vlf antenna tutorial."

For small antennas like this, the Q-factor becomes critical, and the wire in the coil needs to be fairly thick (or use heavy copper tape, or litz wire found on eBay, or even some 1/8" copper fridge-tubing.)