There's nothing verifiably "bad" about the artificial sugar found in sugar-free gum, unless you're eating the fake sugar by the pound every day. It's a lot healthier than chewing sugar-filled gum, certainly.
Many people are alarmist when it comes to artificial sugars, thinking it's more dangerous than real sugar. Other than aspartame ingested in very high quantities, there are no reputable studies that have found causal relationships between artificial sugar and human harm. It can however lead some people to eat more than they normally would when it's taken in the form of a "sweet" beverage, but anyone who controls how much they eat is unaffected.
What will happen: the gum will stick to debris in your mouth and help clean it between brushings. Girls will talk to you more because your breath isn't melting their faces. Chewing sugar-free gum between meals is considered healthy for most people, because it increases saliva and wets the mouth (bad breath is sometimes caused by dry mouth), and it mechanically removes debris by sticking to it.