If by real you mean the kind you get in the supermarket, the short answer is no. First, here’s the ruling, which appears in the directives of a 2004 Vatican instruction (Redemptionis Sacramentum, no. 48):
“The bread used in the celebration of the Most Holy Eucharistic Sacrifice must be unleavened, purely of wheat, and recently made so that there is no danger of decomposition. It follows therefore that bread made from another substance, even if it is grain, or if it is mixed with another substance different from wheat to such an extent that it would not commonly be considered wheat bread, does not constitute valid matter for confecting the Sacrifice and the Eucharistic Sacrament. It is a grave abuse to introduce other substances, such as fruit or sugar or honey, into the bread for confecting the Eucharist. Hosts should obviously be made by those who are not only distinguished by their integrity, but also skilled in making them and furnished with suitable tools.”
The Code of Canon Law (canon 924) and the General Instruction of the Roman Missal (nos. 319-321) affirm this practice. GIRM adds: “By reason of the sign, it is required that the material for the Eucharistic celebration truly have the appearance of food. Therefore, it is desirable that the Eucharistic bread, even though unleavened and made in the traditional form, be fashioned in such a way that the priest at Mass with the people is truly able to break it into parts and distribute these to at least some of the faithful. However, small hosts are not at all excluded when the large number of those receiving Holy Communion or other pastoral reasons call for them.”
According to the Catholic Encyclopedia, we don’t know what the apostles used. It’s possible they preferred the azymous (unleavened) bread used for Passover celebrations, so the Western church tended toward that. Eastern churches preferred fermented (leavened) bread, as they still do. Early on the bread and wine were contributed by the faithful themselves, each contributing their portion. So types and textures surely varied. As reverence for the Eucharist grew, special altar breads were prepared, rounded, and stamped with a religious emblem. These “hosts” became smaller and thinner as the familiar communion wafers we receive today.
• Exodus 12:8, 15-20; 13:3, 6-7; 29:2; Leviticus 23:4-8; Deuteronomy 16:3-8; Matthew 26:17; Mark 14:12; Luke 22:7-8; 1 Corinthians 5:6-8
• The Breaking of the Bread: The Development of the Eucharist According to the Acts of the Apostles by Eugene LaVerdiere, S.S.S. (Liturgy Training Publications, 2007)