I realise it would not make not much sense, but would it have been legally possible?
No. Slaves could not legally contract marriages by Roman law, either with each other or free persons. Slaves were frequently encouraged to breed with each other by their masters, and could have families, but these families and "marriages" were not recognized by law and had no status whatsoever. Masters could (and rather frequently did) have sexual relations, sometimes apparently quite intimate relationships, with their slaves, but they could not legally marry them without freeing them first. Such things were done, but they were often frowned upon--marriages to freedwomen were the stuff of other freedpersons or the lower classes. Cicero attacked Lucius Gellius for marrying a freedwoman, one of the few cases (to my knowledge the only) known where a member of the senatorial class married a freed slave