Can someone get married if they have a power of attorney?

Naming a POA does not in any way diminish any of the principal's rights and privileges; a POA is designated to execute the principal's choices or directions. Some POA documents are activated upon signing and some have one or more "springing" conditions where the POA is not invested with any authority until those conditions are met - for example being determined to be incompetent by one or more physicians. The principal, even after being determined incompetent, retains the right to overrule any POA's action which the principal does not agree. If you want to "force" your wishes on the principal, then you need to pursue guardianship where a court strips the principal of his/her rights and privileges. Until and unless a court strips the principal of his/her rights, they can most definitely marry.