Yes it can happen and happened to me.
I was in my ground blind at 5AM. Very dark but getting things set up. I placed my arrow that i was going to nock standing up against the side wall of the blind. I bent over to pick something off the ground and the arrow fell over against my head (i have a bald head). I barely even noticed that happened and went on my way gettin g set up. Next thing i felt something warm running down my head into my face. turned on the flashlight and wiped my face and head with a towel and it was covered in blood.
Not very deep and about20 minutes of direct pressure and it was completely stopped but i was amazed that the blade did that given how it only tipped over about 12 inches and leaned agains my head.
Magnus Stingers BTW