Would Chewing Gum Have Any Effect At Actually Staining Teeth?

Hi, I have recently done at home teeth bleaching (throught my dentist of course). My usual routine (outside of brushing twice a day) is to rinse my mouth with water and then chew sugar-free gum after I have had eaten or had a drink. I use Wrigleys Orbit or Extra and on some days I can chew 5+ pieces a day, is this okay? Also, I notice that although the chewing gum is white/off-white when I start chewing when I have finished it more cream, would this have any effect at actually staining teeth?