When you dry your soup, your kitchen will be filled with a nice smell of the soup you are drying. That smell is the volatile flavors that have left the soup and are now in the air of your kitchen. When dehydrating apple juice into apple concentrate, that flavor is captured and added back into the concentrate. With your soup its gone. So yes, the soup will have less flavor after drying. How much, and will it be noticable? I don't know, give it a try.
I can't think of a way to overdry something. But you sure can burn things. With commercially dried apples, we started the air temperature at 170, but the fruit was a lot cooler than that because of evaporative cooling. As water evaporated off the fruit, it cools the fruit. Over the 4 hour drying cycle, the temperature is gradually decreased, ending at about 120. If you over dry apples, they are stiffer and crisper, which is not a bad thing. When they are drier, they have a longer shelf life, and are more resistant to molds, yeast and bacteria, because there is that much less water available to support the life of the microbes, and the sugars and acids are that much more concentrated. For drying organic apples, you need them to be stiff and hard, which is about 15% moisture, to make them shelf stable without sulphur or other preservatives.
Vegetables have to be pretty dry, like 4% moisture, so bacteria can't grow. Its pretty darn tough to get them lower than about 4%, because about that much water is tied up chemically, and just won't leave the food very easily.