I am sorry but I doubt any surgeon would every allow that as it could be very dangerous. Immediately post op, your stoma is tiny - even smaller than an M & M plus the swelling from post op swelling and you arent talking much space. If you were to accidently swallow a piece of gum and it will get stuck and could totally block up your stoma which could require further surgery. If nothing can get through, it could be fatal.
At the beginning, you will be on liquids most likely for a couple of weeks, so programs shorter and a few little longer and then you progress to softer foods.. Once you get foods into you, things will move along no problem. It is normal for us to not go for up 5 to 8 days postop because we have nothing in us but a little gum isnt going to push out what isnt in there. You can get things going faster by drinking more protein drinks or creamy soups, puddings. until foods are allowed
Alot of surgeons will tell you no gum ever post op because of possibility of blockage of the stoma but I know my surgeon told us at 1 year it would be okay as long as we are alert enough to make sure we dont swallow it. I basically told him that I hadnt swallowed any in the last 45 years, I dont think I have to worry now but when I hit 80, I will reconsider - he laughed