If Call Management was already ticked in MDM I would imagine it should appear in Console once a valid licence for that module has been applied, however as it's not appearing then I would say running MDM would be a good start. There isn't a great risk of anything bad happening by running MDM anyway. As always though- backup, backup, backup
This was a known issue in Service Portal 7.3.x and is logged as problem 4364. It can be overcome with some manual editing of the database so I'd recommend you log this with support quotiing the problem number and we'll be able to walk you through working around the issue.