I built one of these (a similar configuration from Sci-Toys.com) and it did in fact work at 9VDC. The range was not significant, but I was able to receive audio from the oscillator through an AM radio up to one hundred meters away. Note that the oscillator requires an earth ground and a very long antenna.
http://sci-toys.com/scitoys/scitoys/radio/am_transmitter.html
http://sci-toys.com/scitoys/scitoys/radio/am_transmitter.html