How to tell if a battery pack is draining while in water
At the outset, Lithium-Thionyl Chloride batteries are hazardous (HAZMAT Class 6.1?).

The electrolyte Lithium 4-Chloro Aluminate (LiAlCl4) reacts with water. Therefore if there is contact with water, this answer assumes appropriate precautions are being taken. Since Li-SOCl2 batteries are not commercially sold (AFAIK), the application in question is probably industrial or military, so OP most likely knows all this. The caveat is for future readers.



The following steps may be used to profile whether and how much the battery is being drained by water:


Determine the approximate average current draw I of the device under normal (not compromised in water) conditions, either by measurement or estimation
Calculate the resistance [Note a] that would be needed to draw the same current from the battery: R = V / I, where V is the nominal voltage of the battery, 3.5 Volts for single-cell LTC batteries
Take two cells of identical charge state and voltage: measure (and log) the voltage to confirm this - If there is a mismatch keep checking till you find a pair that match as closely as possible
Log the precise time, connect a resistor of the calculated value across the terminals of one of the batteries. Leave the set-up (sub-points below) alone for about two-thirds the expected run-time of the device per battery: that should provide enough data. 

If you have access to a very high-impedance logging voltmeter or an oscilloscope with 100x probes (not the basic multimeter, as that would consume a discernible current itself), set it up to log voltage over time. 
If a high-impedance voltage measurement option is unavailable, simply measure the voltage after disconnecting the resistor and "stopping the clock"each time, once every 10% or so of the expected run time. Note that this will introduce some small error into the experiment

Repeat the above experiment with the other battery of the matched pair, but with the set-up in the submerged operating condition intended for final deployment. 

Presumably the whole set-up is in some form of hypothetically waterproof enclosure, otherwise direct measurement and logging will give invalid results due to the probes themselves being in water [Note b].
If the device is expected to operate in direct contact with water, then the continuous logging proposed above is not an option, the timed logging approach must be followed: Extract the set-up each time, dry it out and measure voltage, with the clock stopped for each measurement

Repeat steps 4 and 5 for additional matched pairs of batteries, if a larger sample set is desired.
This exercise should provide a clear mapping of difference in battery longevity between the submerged and in-air modes. [Note c]


Please post a comment if some aspect of the above represents an incorrect assumption, and I will update this answer accordingly.



Notes:


 a. The use of a passive resistor precludes any discharge profile differences due to varying power draw by the actual device over time.
 b. Ultra-pure distilled water has reasonably high resistivity, ~ 18 mOhm.cm. However this varies with temperature, and impurities such as possible contamination by the battery electrolyte will have significant impact
 c. Operating temperature itself will change battery life, the resistor's resistance, and may change the device current draw as well. Hence, if possible the in-air and in-water parts of the experiment must be conducted at similar environmental temperatures.