Good question... so I dug out my DVM. The answer is, yes - if you replace starter relay #1, as the directions tell you to. This starter relay gets its feed straight from the battery, and as such, the Mobilistics relay is drawing current all the time. However, it's only drawing 33 or 34 mA (my meter couldn't make up its mind - so call it 34mA). With a typical reserve capacity of 60AH, that would take over 1700 hours to drain the battery. In a weeks time, it would pull 5.7AH out of the battery, or a little under 10%.
However, if you were concerned, you could replace starter relay #2 instead, as starter relay #2 is powered by starter relay #1 (see attached diagram). Starter relay #2 is directly above starter relay #1 in the PDC, looking it at from the side of the truck (#2 is closer to the engine than #1).
I confirmed that all functionality works with the Mobilistics relay in position #2, and thanks to you pointing this out, I'm going to leave it in the #2 position - I don't like extra parasitic draw either, no matter how minor.
I believe Mobilistics advises replacing relay #1, due to the added complication of remote start. With the relay in #1, you can remote start by EITHER pressing the Mobilistics transmitter, then activating remote start on your keyfob - or the other way around. Doesn't matter, because in position #1, the Mobilistics relay always has power.
BUT - with the Mobilistics relay in position #2, you HAVE to activate remote start FIRST, so relay #1 can power up the Mobilistics relay. Only then, AFTER giving the truck about a second or two, while it's silently TRYING to crank the engine, can you hit the Mobilistics transmitter to engage the smart relay, and start the truck. It's a timing thing, and if you goof it up, remote start will disable itself until you start the truck manually.
So take your pick - add 34mA to your ignition-off draw, and have convenient remote start, or eliminate the parasitic draw, while slightly complicating your remote start sequence. Life's full of choices, right?
View attachment 33359
(in the above diagram, fuse #40 is fed directly from the battery - and the output of relay #2 goes off to the left to the starter. The Mobilistics relay draws it's power to operate from pin 30)