Even in the sixth grade, our students ask this question frequently. On the surface, it would seem that it would be okay for an engaged couple to engage in sex because they are obviously committed to each other. But the question is: Are they committed enough to express the true meaning of sex?
God created sex to have a meaning. In Pope John Paul II's theology of the body, he discusses the concept that our bodies "speak" a language that is meant to point us to God and our desire for union and communion with Him. Sex, then, is meant to express through the body what wedding vows express through words.
In a wedding, the priest asks if the couple has come freely and without reservation. Therefore, sex is meant to express love that is freely given.
During wedding vows, the couple promise "to be true to you in good times and in bad, in sickness and in health. I will love you and honor you all the days of my life." They also say, "I promise to be true to you … until death do us part." Therefore, sex is meant to express love that is total (holding nothing back) and faithful (committed until death).
During the wedding, the priest asks the couple, "Will you accept children lovingly from God and bring them up according to the law of Christ and His Church?" Therefore, sex is meant to express love that is fruitful (not referring to pears and oranges but to an openness to new life).
When a couple is engaged, they are planning to commit in this way, but they have not yet done so. I have several friends who were engaged but broke up before the wedding took place. Until the wedding vows have been spoken in front of God, each other, one's friends and family, then the couple is not capable of honestly or authentically expressing the true meaning of sex. So, the answer to this question would be, yes, it would be wrong (and not practicing chastity) for an engaged couple to have sex.