Well.... on the S&S site it says in the bit about VLCDs-
I seem to have a bad breath?
A mild ketosis may develop when on any very low calorie diet and this may affect your breath slightly. Simply brush your teeth more often, and use mouth wash, sugar-free chewing gum or breath fresheners.
However I asked the same thing when I started and got the answer from most not to have it. For one reason chewing may make you hungry, but I know thats not the case with me as I use gum NOT to eat! The more important thing is that chewing on a VLCD, with an empty tummy, makes the stomach produce excess acid which puts you at risk of an ulcer.
I've chewed the same brand of gum for 20 years or so, since I was at primary school! But since I started S&S I stopped. I have 2-3 Smint mints a day because they are the smallest mint I can find and I need SOMETHING! They are really high carb though, I have yet to find a low-carb sugar-free mint, sigh.