Actually, no the law cannot. As we have seen with several states recently, the law cannot under their state constitutions define marriage as between a man and a woman.
Similarly, with these same problems in defining them however they want, there will be problems with defining them against people of age of consent- even if they are directly related, multiple spouses, authoritative figures and subordinates and so on. So eventually, we might end up seeing not only a brother marrying his sister, but his other brother, school teacher, and widowed mom too. If they do not reproduce, there is nothing technically medically or scientifically wrong about that either. There would be no overriding policing authority for the states to impose such limitations which seems to be how legally defining marriage only between a man and a women was defeated in most of the states which the courts made marriage legal.
You might ask why would someone want to marry their sister or mom or more then one spouse if they aren't going to reproduce. That answer is simple, death taxes and other benefits like being added to insurance or medicare or social security payments. The supreme court rules against the Defense Of Marriage Act (DOMA) due to estate/death taxes being challenged. So we already know it is a reason or part of one that people want to become married.