Larry Fine himself says on the Three Stooges Story DVD that the tip of the fountain pen indeed punctured him and he let Jules White have a few choice words afterwards.
In Larry's words, as published in Stroke of Luck:
For this trick, they had attached to my forehead a tin plate, with a hole in the center, and attached to the tin plate was a spring wire that was to direct the pen to the hole in the center of the plate. The idea was that at the moment the pen "pops" from the bowl, the prop man would throw the pen attached to the wire at my forehead, and it was supposed to stick to the center hole.
I protested that the hole in the center of the plate was too large, and that the pen would go through it and I might get hurt.
"Oh no, Larry, everything will work smoothly," said the director.
At the moment of action, the prop man throws the pen, it goes through the center hole, and sticks in my forehead. I pulled the pen out of my forehead, and I was bleeding like a stuffed pig. Needless to say...I wanted to kill the director!