Probably not - otherwise we wouldn't be using RO and rain water for our plants; they'd be doing great in tap water.
My plants in pots get K-lite at about 10-15 ppm N in RO water (10-12 ppm TDS), total TDS reading is about 70. They're doing fine and are not showing any signs of nutrient deficiencies. Each new growth is bigger than the previous one, whether it's cattleyas, oncidiums or phrags. Everything is in balance, although at very low concentrations.
The plants on my living walls get ammonia-based 25-10-10 also at 10-15 ppm N, with added Epsom salts, for a total TDS reading of about 90-100. Since the walls are concrete based, the plants get plenty of Ca, and I need to add some Mg to balance it out. The actual amount of Ca is not nearly as important as the Ca/Mg ratio, which should be in the 2-4 range. The runoff water has a TDS reading of about 300, so it picks up a lot of calcium. It also picks up silicate, iron, aluminum, sulphate and a whole host of metals from the flyash component of my concrete.
Flyash is the leftover minerals after the organic components of coal are burned off. It's about 1% of the weight of coal, so the trace minerals in coal are concentrated 100 times. Still, they're in the same perfect balance as they were in the ancient vegetation that created the coal deposits.
I'm growing phrags in the catch basin of my newest living wall, in semi-hydro conditions in lava rock, and they seem to be ok with the 300 ppm TDS water that they get. I do flush them once in a while, though.