Yes they can bleed. A cold sore is a herpes simplex viral infection that occurs most commonly on th lips of the mouth, but can also occur on the penis and vulva, and other places of the skin. During the first stage, they produce a tender sore, that can then form a scab and bleed. Use vaseline to keep the area moist, and try drug- store medicines for cold sores, or get a prescription for acyclovir.
Yes. Cold sore, which are ulcerations caused by herpes virus, can crack and bleed. They start as a vesicle (blister or bubble filled with fluid) that rupture and seep infectious serum. As they scab or crust over, they may tear and bleed.