Dear Hilary,
No, the non-Catholic may not receive Holy Communion at a Catholic wedding. Actually, not all Catholics may receive Holy Communion. Only those who are in the state of grace (no unconfessed mortal sins) and are married in the Catholic Church may receive.
To receive Holy Communion in the Catholic Church is a sign of complete acceptance of Catholic teaching. It is also a sign of complete unity among believers. Unfortunately, Catholic and non-Catholic Christians still do not share such unity. So it would not be an honest sign.
This is why Catholics who are marrying a non-Catholic are usually encourgaed to not have a Mass with their wedding.
Fr. Vincent Serpa, O.P.