The main drawback of giving the cereal is that it is not necessary. While it is true that it is unlikely for there to be any real harm to the baby from having the cereal, very rarely infants can have adverse reactions (like allergies) to cereal.
The other thing to consider is what are appropriate expectations for a three-week-old baby. A three-week-old is supposed to wake and eat every three to four hours. It is not until about three months of age that we expect babies to sleep for six or seven hours at night.