InuYasha frequently stops what he is doing and saves Kagome if she happens to be in danger. This has even limited him in his ability to kill Naraku (something that is obviously very important to him). It could easily be argued then that he is willing to sacrifice his goals out of feelings for Kagome. As for Kagome, she gave up her life and family to go live in the feudal era. This could very well be because of her feelings for InuYasha. So, it seems that yes, they may be ruled by their emotions deep down.