Not necessarily, if Rin had enough Power Cores, she can overpower Muramasa and actually execute a pretty cool move.During the Stallion Trial, there's a scene which you'll get if Rin passed the previous trials and you choose not to go into the town during the start where you and Rin gets into a fight. One of the options there is to throw her your weapon to use because you currently are unable to use aura.
Fun fact: If you were using Muramasa during that and throw it to her, she gets insta-possessed by it.