The commonest sugar alcohols (sorbitol, malitol) seem to have around half as many calories as sugar. I assume that the part that’s absorbed acts equivalently to sugar.
A piece of sugar free gum may have like 3 calories per piece. I don’t think it adds up to much, even in Stu’s case.
Sugar alcohols do affect blood sugar in a manner that any other carbohydrate would. The calories per gram, however, are a bit lower. Most sugar alcohols that are used in gums are anywhere between 2-3 calories of carbohydrate per gram. So if you’re chewing a whole pack of orbit gum, that’s 14 pieces multiplied by let’s say 2.5 calories, which gives you 35 total calories of carbohydrates. That’s like just over 8 grams of carbohydrates that you are consuming in a day. Not a whole lot, but if you really low carb or trying to go ketogenic, it could have an effect but I doubt it.