The human mouth contains trillions of bacteria, microbes, dead skin cells, fragments of food, etc., & ambient air contains fungal spores, pollen, dust, lint, insect parts, & more bacteria. The reed & neck cork are porous environments frequently inundated with warm, moist, microbe-laden air. Although individual results will vary with location, climate, local flora & fauna, it's absolutely certain that cooties are thriving in our apparatus.
I'm no germophobe, but I do brush before playing. It makes my mouth feel cleaner, & reminds me that making music is an honorable pursuit that deserves respect. After playing, I swab moisture out of the sax body & neck & mouthpiece. From time to time I wash mouthpieces in warm water with mild soap, & give reeds a brief rinse with hydrogen peroxide. Can I prove that these practices benefit my health & my gear? No. Do I need to?