I don't think it could hurt, but sometimes principals don't care. When I was student teaching, my cooperating teacher thought very highly of me and would tell me that she made little remarks to the principal all the time about how good I was. I won an "Outstanding Student Teacher" award during student teaching (I was nominated by my university supervisor. There were only 10 winners out of a couple hundred student teachers so it seemed impressive at the time.
) and she went and showed him the award, LOL. She convinced him to come sit in on one of my lessons.
In the following year, there was an opening for a kinder. teacher and he interviewed me for it. During the interview, he seemed totally disinterested - kept looking at the clock. He told her afterwards that I interview well and he thought I was a good candidate, but he wanted someone with real teaching experience.
But to answer your question, I don't think it makes you look desperate. If anything, it shows how much you want the job which is a good thing!