Your driver is probably a buck driver with a set constant current of about 1.7 amps or so. You can look at djozz test with the XHP50.2 and see were 1500 lumens are at in current to the led assuming its 6v version.
Thats just a rough estimate but should be some what close to the led. With a buck driver the voltage is higher than the led vf. So if you have twice the voltage of the vf of the led the driver would only need to pull half the current from the cells to operate the led at twice the current drawn.
12v battery x 1 amp draw = 12 watts to a 6v led
6v battery x 2 amp draw = 12 watts to a 6v led
That means your probably only drawing around 1 amp with the cr123 and around 1.4 amps with 2 18650’s, just a guess.
Adding a bypass wire will probably do little to nothing for this light.
Most of the time a bypass wire is added when your using a fet driver where its direct drive and ever little bit of resistance determines the current as well as the battery used.
Anytime you have a resistance you have a voltage drop and looking back at djozz graph you can see you need a specific voltage to reach a certain current. If you loose to much voltage from resistance (voltage drop) in the circuit you dont have enough voltage to reach but a certain current.
I have used boost drivers that could draw upwards of 15 amps from a single cell and that is a good place to use a bypass wire also. Its having to boost the voltage and any place you can avoid to much voltage drop helps keep the voltage high for good output. It also can heat the spring up to a melting point if a good low resistance spring isn’t used.
I would guess to say anything running a single cell or multiple cells in parallel would benefit from a bypass wire around 5 amps or more. With a buck driver its not going to be needed unless its putting out some serious output.