Is it safe to let my baby fall asleep after he has had a serious fall?

Yes: If he seems otherwise fine, it is ok. However, after ~1 hour you should rouse him to be sure that he can reach a normal level of alertness.

Yes: This obviously depends on the seriousness of the fall, and what happens afterwards. If the child falls 1 ft onto carpet, and looks fine, then yes. If the child falls 12 stairs onto hardwood or cement, then a thorough monitoring period or check in the ED is required. If there is no loss of consciousness, and the child is consolable, looks ok for a couple hours, and behaves normally, then yes.

No: If a baby has a "serious" fall, it is not "safe" to let him fall asleep without an evaluation. Realize that it is impossible to not allow a baby to fall asleep. Trying to keep a baby awake will create a strange behavior (the baby will be tired, fussy, and sleep-deprived). The important thing is to get the baby to the hospital er so the doctors can evaluate for injuries from the "serious" fall.

Yes: After a serious fall, your child should be examined by a medical professional. If they determine that there is no brain injury then allowing your child to sleep soundly through the night is no problem.