What could be the result of the parents of a girl who is over 18 filing a complaint against her boyfriend who is also over 18 because she left home without their permission?

The would probably be no "result". I dont know what state you are in been the general age of adulthood is 18, 17 in michigan. When they are of age you have no legal recourse against her or her boyfriend. But, your local police dept can answer your question over the telephone.