Why do you put celery in a bloody mary? Is there a chemical reason for this or is it done just for garnish?  
It's meant to be munched on between sips, and permits a "reset" - the cocktail will be fresh upon the tongue the sip after the bite, permitting you to enjoy its flavor and consistency without being oppressed by the cumulative effect of unctuous, spice and salt that is the hallmark of the beverage.   Celery is an astringent and an aromatic - it will cut through the palate-coating tomato juice can leave behind, cool the intensity of the salt and heat, and will interrupt the soup-like consistency with a firm crunch. It's often included in tuna and chicken salad and served with hot wings for the same reason. Other vegetables that tickle our sense of "bitter" in a pleasing way may be similarly substituted - but celery also acts as a handy swizzle stick.  