No, I don't think that a dip pen is likely to slow down an encroaching zombie. Sure, it's nice and sharp so maybe I could use the pen to stab the zombie in the brain, but I'm not sure it would penetrate through the skull into the zombie's brain on one shot, and I'm not sure the pen is strong enough to retain its shape and sharpness for a second stabbing attempt. Or maybe I could pour the rum from my hip flask onto the zombie and then use the matches to set the beastie aflame, but there's less than eight ounces of rum in there. Not sure that would make an effective enough, or large enough, flame to bring the zombie to a stop.
I have a feeling that if a zombie cornered me at my desk, I'd be seriously out of luck.