What could happen if a night guard was accidentally swallowed?

Impossible 4 most. Normal night guards are too big to be swallowed. Smaller ones such as the nti could result in swallowing. What happens? They will pass out uneventfully or have to be surgically removed. Your body has reflex mechanisms that will in almost all cases, prevent accidental swallowing or aspirating of foreign bodies.
Stomach/bowel problm. Depending on the size and material, anything from nothing to mild irritation to perforated / obstructed stomach / bowel. If this has happened , get to md or E.R. For evaluation.