Nope:
People mistakenly assume that a falling penny, subject to the force of gravity, will accelerate for the entirety of its fall, achieving breakneck speeds by the time it reaches the ground. This would indeed happen if New York City was evacuated — that is, if all the air were removed and the penny was tossed off the Empire State Building into a vacuum — but as things are, collisions with air molecules slow falling pennies down.
But a ballpoint pen could:
Depending on their design, pens will either spin and flutter, or shoot down like an arrow. In the latter case, "it might well come down at 200 mph," [physicist Louis Bloomfield] said. "When it hits, it will hit a small area with a lot of momentum. It will chip the sidewalk. It could punch into a wooden board. You wouldn't want it to hit your head."