If you are near a very powerful station, say 10, 25 or 50kW (!), an arrangement like this could probably be heard at much greater distances. The transmitters for most Cleveland AM stations, for example, are located in a west-side suburb of the city, and if you are anywhere near them, an amplified crystal set tuned to any of them would probably be so loud as to be annoying, if not downright unbearable; an ordinary free-power set probably could drive a small loudspeaker to a decent listening volume.
The other problem with all crystal sets is poor to downright non-existent selectivity. If you are very near one or more high-power stations, your galena-crystal radio would have the heck of a time separating the signals; in fact, I think you would only hear a mishmash of noise, as your set received all the stations at once. I had a Remco crystal set when I was a kid. The radio worked well enough (using a 50-foot wire antenna in my back yard) to receive the local station in the next town west of me, and I'll never forget the time when, after that station signed off (it was an 0.5-kW daytime only station at that time, late 1960s-early seventies), I actually heard a faint signal from a top-40 rock station in the city of Cleveland, the transmitter being in a western suburb. The station itself was not that powerful, either, only running 5kW daytime and, IIRC, 1kW or less at night. I was living at the time in a Cleveland suburb some thirty miles from the transmitters of all the city's radio and TV stations, so I was surprised -- nay, astounded -- to hear that 5kW station on a crystal set, albeit faintly, like a gnat sighing through a window screen at 10 paces. The only thing I can figure is the propagation conditions that night must have been unusually good. Never heard any other Cleveland stations on that Remco free-power radio, though, and the radio itself is long gone.
I hate to think how loud Cincinnati's WLW must have been on crystal sets when that station was running its 500-kW transmitter in the 1920s-'30s. A plain crystal set without an amplifier would have picked up the station with room-filling volume, and then some; one could probably use a speaker in place of headphones easily. However, I would hope that any crystal set driving a loudspeaker, with or without an amplifier, would have some sort of output limiter or even an actual control to allow the listener to reduce the volume if desired or if necessary -- especially if listening to a close-by 50-kW station.