Batteries and running time
In general connecting batteries in parallel is a bad idea. Such a parallel connection violates a basic rule of electricity. Parallel connection works for certain types of batteries, but is a disaster for others. 

Here's the problem: A battery is a voltage source. As such it will attempt to deliver its generated voltage at whatever load is connected to it. When two voltage sources are connected in parallel, each will try to deliver its voltage to the other battery. If the batteries both have the same exact voltage, the net current flow between the batteries is zero. If the voltages are not exactly equal, a current will flow from the higher voltage battery into the lower voltage battery. The magnitude of this voltage follows Ohm's Law. The resistance/load in the simple connection of two batteries with no external load is the interconnecting conductor (e.g. metallic battery holder) and the internal impedance of the batteries. Since both of these impedances are quite low (generally fractions of an Ohm for the holder and a few ohms for the batteries, the resulting "cross current" can be quite large compared to the magnitude of current the batteries are designed to deliver to a legitimate load. 

The other effect is that the lower voltage battery will have a reverse current flowing thru it (again by virtue of Ohm's Law). Not all batteries can tolerate such a situation. Rechargables generally can because they are designed to be charged, However, one-time use batteries are not designed to withstand reverse current flow.

Typically, the end result is a relatively rapid discharge of both batteries with a variety of side effect depending on the type of battery chemistry. Heat generation is one common side effect. In certain situations the heat can be great enough to thermally destroy the batteries.

The only salvation is that the two batteries might be perfectly matched both in initial voltage (e.g. as manufactured) and remain matched as they discharge over time. Or, the battery chemistry is such that it can accommodate the voltage difference and both batteries will work in unison to develop a shared operating voltage. Lead acid batteries can do this. Common alkaline batteries are not so accommodating.  I'm not sure about your CR123 units. However, their current rating is high enough that I would perform an experimental parallel hook-up without a load, and in a safe, contained situation where I could terminate the connection if things get dangerously out of control.