We all have different reasons for IF. What is your reason?
Are you looking to only lose weight? Then maybe its ok. If you can go without it thats best. If you need it now or you would end up snacking on a bunch of junk then yeah go for it.
5 times a day though is a lot. Gum is a confection meaning it is more of a dessert item based on sugar content. For fasting sugar free is better. Try to ween yourself off the gum too. If your first piece is normally at 8am. Try to push it back to 9am. As you push the times back start to drop off a piece once the time enters your eating period. Jeep going until you don’t need it at all.
The longer your body can go without insulin the better your results will be. This is essentially the same question about artificial sweeteners in black coffee.
Is it calories, no. Is it preventing your body from burning fat, yes.