Highly unlikely unless you've got a pre existing blood condition where you don't clot. I have frequently cut several veins in my arm so that it pours out, not just dripping, and even when I was deliberately taking aspirin to reduce clotting, each time the veins stopped of their own accord. I've passed out twice from it, threw up a perfectly good steak and ale pie and chips, and am now badly anaemic - but still alive and kicking.