Is it illegal to get married to a person you have a no contact order with?

No, it is not illegal. However, due to the very nature of the "no contact" order the parties should engage in some premarital counseling, perhaps through a victim's advocacy agency. It will be difficult to plan the ceremony if one cannot be present due to the order. They should also remain apart as long as the no contact order is effective unless they request an early termination from the court that issued it.