If the Zero doesn't strip your water down to RO, it's probably fine. I don't know what mineral cocktail makes up "Third Wave." I'll look, but I doubt it's going to tell me. Bottom line, if your filtered tap water tastes good, it probably will make good coffee. But if you strip your water bare of all minerals (RO/Distilled), it's like eating an unseasoned steak. I understand it a little better when it comes to beer, but I'm guessing the amount of calcium in the water as well as the ratio of chlorides to sulfates is important to the extent it accents the sweetness and the bitterness of the beans. I tried one of those water treatment packets when I was brewing beer and it was more an acidity adjustment for ideal mashing. Ultimately, I sent my filtered tap water to Ward Laboratories and, for $10, I had a water report that allowed me to doctor up my water for a variety of styles or blend it with RO for some more delicate styles.
Edit: Third Wave is formulated with magnesium sulfate, calcium citrate, and sodium chloride. That's all fine and well. Those are the minerals you want to have in various proportions in a good brewing water profile too. But if you don't know what you're starting with, even having blends for different roast levels doesn't take into account your starting point and, therefore, is basically useless.
I zip tied my cables that touched the floor to the underside of my console just to keep the robot vacuum from eating them.