Yeah, they’d bleed out all right. So, when we talk about blood loss from arterial injuries being dangerous, the issue is the speed the volume is lost at, not that the artery itself is somehow special. Rupture enough veins in the legs and they will bleed to death. It might take a few minutes longer, but it will kill them.
I’m inclined to say it would actually be more dangerous than an arterial injury. In that case, if you can get medical attention there’s one injury they need to deal with. The situation you’re describing would result in hundreds of simultaneous injuries that are dangerous as a whole, but treating them individually would be extremely time consuming, and by the time they were done your character would have bled to death.
Also, yes. Hypovolemic shock is a function of the body shutting down from blood loss. If you start losing a lot of blood you will go into shock and die.