Will they? Or do they never get a chance to coagulate, thus remaining open forever?
I hope an expert drops by but for now I’ll throw in that blood doesn’t clot just from drying up, it clots from the accumulation of platelets at the site. So I would guess that all other things being equal, a cut that would stop bleeding in open air would also stop bleeding underwater, although maybe not as soon. So I hope there are not sharks down there with you. . . . .
Yes they stop bleeding. Just like CookingWithGas said, the clotting is due to rupture of platelets. These things will rupture if dehydrated, but they also rupture from passage over rough surfaces like the edge of a wound. Whent hey rupture they create ‘strings’ within the blood. These strings trap blood cells and gunk and form the clot. Underwater the string gets washed away, so the clot forms a little slower and tends not to be as strong, but it still forms.