The non-coughing proctor is Shiranui Genma. And yes I think Baki does fight him but the fighting is not shown in the Naruto anime episode.
Here's a link to a video with part of the scene with Baki and Genma: http://www.youtube.com/watch?v=MIfwydvkQ3E. It's episode 68, ""Zero Hour! The Destruction of the Hidden Leaf Village Begins!".
In the video, Baki tells Temari and Kankuro to bring Gaara away to rest. And when Temari asks Baki, "What about you, sensei?", Baki replies, "I will stop these guys".
And later on in the episode, Genma tells Sasuke to chase after Gaara. So after the Sand Siblings and Sasuke have left, Baki and Genma are left facing each other, so I would think that they fight with each other, although we don't get to see it.
Yup hope that helps! :)
Wikipedia, YouTube, and also from watching Naruto! :)
· 1 decade ago