Is it true that when an alcoholic stops drinking suddenly that he would get sick?

Yes, withdrawal can be deadly. It can cause uncontrolled seizures and all sorts of scary things.

“Alcohol withdrawal symptoms can begin as early as two hours after the last drink, persist for weeks, and range from mild anxiety and shakiness to severe complications, such as seizures and delirium tremens (also called DTs). The death rate from DTs—which are characterized by confusion, rapid heartbeat, and fever—is estimated to range from 1% to 5%.” Source

Pink elephants, snakes and bugs; are all common hallucinations from alcohol withdrawal. some people will go into seizures and yes death.

I just wanted to clarify that my answer is more of a could than would. Most alcoholics go through some sort of physical withdrawal symptoms, some more severe than others. It’s advised that withdrawal is supervised by a medical
professional.

When the father of a friend of mine died I suspected the hospital not treating him with alcohol was a contributing factor. I found out how he died after the fact. He had become ill, he had been a diabetic for many years and from what she told me initially his hospitalization was related to that, but then she stated, “they couldn’t get him to stop seizing.” I never said anything, but I can’t help but think they let him withdraw while in the hospital and no one figured it out, or the doctor didn’t treat it correctly.

I had a friend who is a nurse and when she switched from county to a private hospital out in the burbs, she was shocked at how different the hospitals were at treating drug withdrawal. The county hospital had a method to help the patient, taking withdrawal very seriously, and the private hospital basically just tried to manage the withdrawal, but in her opinion not nearly as effectively, and it was never given any sort of primary focus.

Yes, severe alcoholics go through DT’s, and that can kill them in extreme cases.
That said, Amy Winehouse didn’t die because she stopped drinking. She died when she started again.