Should a 7yr old find it painful when adult teeth come through?

Possibly. Just as infants have teething pain , kids who are getting molars can describe some discomfort. If when erupting some tissue forms around the tooth they can end up with an infection called pericoronitis. This happens more commonly around wisdom teeth.
Teething can hurt. Teething can be uncomfortable for any person of any age. It is usually mild and bearable.