in fact, as a kid i got a lot of mild lacerations, sometimes quite severe, from skateboarding. i never did anything about it, except if it wouldn't stop bleeding. healed up just fine in a few days and then itchy and scabs fall off.
i wouldn't advise this in general, really you should always wash a bleeding wound thoroughly, and apply disinfectant, and seal it up and bandage over it. plastic is actually better, doesn't stick to the blood, but after giving myself a good minor vein cut last year i always keep bandages, band-aids and gauze and antiseptic cream in the house. on that occasion i had to rip up a shirt and use plastic while i went to pick up those supplies. it was pretty bad, i was starting to go into shock from the blood loss.
so i make it a rule now. in fact i really should make a small pack for my backpack when i go on big walks. just haven't really been fit enough to tackle the terrain here, most places i ever lived were not nearly as rugged.