No, I'm not sending the signal levels right now...should remember to add this in my code sometime soon.
According to the manufacturer information the voltage should remain extremely steady over their lifespan, only dropping when very close to the end...but I will certainly keep monitoring it. At the moment I can call Particle.connect() for several minutes and the batteries will still remain functional.
However, this doesn't fully answer my question yet; will I hit 800mA as long as I'm calling Particle.connect()? Regardless of battery voltage and such, since 800mA is a insane amount, if it remains that high throughout the entire connection process then being able to connect ASAP would have to be a very high priority to extend the lifespan of my sensor