Usually no. Laser is picking up pigment in the hair and most peach fuzz (even if it looks like it has a fair amount of pigment) usually doesn't have enough pigment in it to be picked up. The peach fuzz is so fine that even with pigment the laser normally cannot pick it up.
I know that many woman get nervous about shaving their face but shaving will not make the hair thicker or darker. When you shave or trim hair you are only cutting off the ends which do not affect the follicle. You need to affect the follicle in order or affect the hair. When you pull a hair you are actually stimulating the blood flow at the root which can make the hair worse. When you laser the hair the laser is damaging the follicle.
Shaving the face is actually good for the skin. and dermablading is great way to do it. The dermablade is just a blade with a handle. Dermablading is the process of gently scraping away dead skin cells and "peach fuzz" hairs which gives your skin a smoother, brighter complexion. You can buy one at your local drug store or online.