Great question-to a basic approximation the answer is no, as the transitions have different symmetry. However, this is possible via internal conversion or intersystem crossing if the energetics are right and a vibration can mediate the transition (vibronic coupling).
Is it possible that the engery required for π→π* transition can also promote n→π* transition, since E(n→π*) is lower than that of the former?
Great question-to a basic approximation the answer is no, as the transitions have different symmetry. However, this is possible via internal conversion or intersystem crossing if the energetics are right and a vibration can mediate the transition (vibronic coupling).