It isn't necessary but you can try it. What do you have to lose, you are already banned. Worst thing - you remain banned forever. Anything less than that (like a temp ban or a signature ban) is a plus in your book.
You are a newbie and maybe the staff you are planning to contact have disabled the possibility of newbies PMing them.

What you can do is explain what good you have done for the forum since you have been here and how the forum would benefit if you are given a second chance. If the staff like what they see, they might reconsider the ban...