Not a simple answer. I guess the best one is... it can for some.
Sometimes the sugar alcohols used can cause some diabetics just as much grief as "real" sugar, if not more (because their chemical compounds can be so complex and can affect various different body functions). Often the sugar-free stuff still has carbs in it (like 1-2 grams/piece).
Diabetes is an endocrine (think: hormones) and metabolic disorder/malfunction (how we process or metabolize food).
Then there's the body's natural digestive process that kicks into gear as soon as saliva starts production. Without getting technical, the body's metabolic processes start: hormones (insulin, cortisol, etc) and stomach juices are waiting for that "food" that doesn't follow through (you don't eat gum
On an empty stomach, this can cause gastrointestinal distress and in some, can cause an increase or even a decrease in BGL. Chewing AFTER a meal would lessen those effects but there's no guarantee.
For the record, I like that gum, too but I try to "use" it more as a breath freshener/teeth cleaner after a meal; getting rid of it within 5-10 minutes