The EOS runs off of 3 x AAA batteries which is 4.5 volts and one CR123 battery is only 3 volts. The EOS is regulated so it probably uses a buck circuit. Using a 3 volt source would require a boost circuit.
Ok... just tried it out.. didn't want to say anything without testing it. The EOS does turn on but when I measure the output on my lux meter it puts out only around 25% of the output of the 3 AAA batteries. I would try two CR123 batteries but I'm afraid it will fry the circuit.
It might work better with an RCR123 since they are higher voltage but I don't have one to test.
Sounds like it runs direct drive on CR123 since it is under the LED Forward Voltage.
I have though a mod of the EOS to use an RCR123 or 14500 would work since it is about the correct voltage. If I REALLY wanted one, I would model up a body to transplant the electronics and have it made via stereolithography or other rapid prototyping.