That’s like saying you have a limited amount of muscular endurance per day. It’s true, but it’s completely trainable. Meaning just like you can go from barely able to run a mile to being able to run an ultramarathon, you can do the same thing with your willpower. But unlike running a marathon, training your willpower will yield real, life improving tangible benefits assuming you can correctly figure out how to apply it for your benefit. Maybe a poor analogy because running an ultramarathon requires lots of willpower :)
Regardless of whether one accepts the arguments in the comic, I doubt willpower can be trained. It's not like a marathon where you have to actually run to practice, every day you're faced with decisions and temptations that you can "exercise" your will power with. In a sense you can't really stop practicing with your willpower...