No, it simply passes through the digestive system, and is discharged as a waste product. A lot of kids, myself included, were always told that swallowing chewing gum was harmful, probably a byproduct of inherent parental distaste at the habbit of children chewing it.
I was told that the juice produced by chewing gum makes the body think it is about to digest something but yu are not so it is not good to chew gum let alone swollow it.