My puppy has underbite but she doesn't bite more. An overbite or underbite shouldn't affect a dog's ability to control its bite pressure. If anything, either condition might decrease (slightly) the amount of pressure they can apply compared to a dog with a normal jaw.
An underbite or overbite shouldn't affect a dog's teeth or jaw health, generally. Each case is different though.
Just don't let your puppy get away with mouthing you too rough because of its overbite! Maintain the same expectations you would for any other puppy.