I would like to share an anecdote. In March 2016, I was weighing 96 kilograms (211.64 pounds). I made just one change during that time which is to stop having anything with sugar. I continued to take other natural sweeteners like jaggery and honey. The rest of my diet remained the same and my activity level remained the same ( I work in IT as a network engineer in a desk job) In October 2016, I was weighing 72 kilos…
You must mean "stop having anything with added sugar" because humans need sugars to survive, nearly all food has natural sugars in it, and if you ate 0 grams of sugar for more than a couple of weeks you would die. I'm being a bit pedantic because it's important to understand that moderation is the key, not trying to completely eliminate one family of molecules from your diet.
No you absolutely would not. Your body can synthesize glucose from protein and fat, you can survive indefinitely on zero sugar. This is called ketogenic diet.