Most sugar-free gum uses some type of sugar alcohol (e.g. xylitol, erythritol). These are not technically-speaking considering NAS. Their mechanisms of absorption vary wildly and, while in some cases they can cause digestive stress in large amounts, there is no good evidence AFAIK that they have a deleterious effect on gut microbiota.
At first I thought, yeah, this will never be a problem for me, then I realized the only thing I do consume with artificial sweeteners is gum. I do hope the doses are low enough not to be a problem, but I want to know!