I would say definitely not. If you are sure you want to, I would first get the approval of several people. Like if you are really confident you can provide a funny reply that is good, give it to a few English professors to approve. If they say it is really good, and wouldn't be inappropriate for this, then maybe so.
I don't think there is anything wrong with a good sense of humor as long as it is tasteful, adds to answering the question posed, and helps round out your personality. Trust your gut, however. Say it out loud to yourself or to a trusted friend/advisor and get a feel for the tone that comes across. I generally abide by the premise that if I don't get a whole-body "yes" about doing something, it's probably not a good idea to proceed with it. Make sure you aren't writing it out of some unconscious motivation that could bite you in the butt. Otherwise, it's probably cool and might even come across as refreshing to the adcomms who read dry and prosaic stuff all too much.