Well we can gather quite a bit of information from the old Phineas Gage story.
*1850ish he had an (artifact) iron rod shot through his head in a relatively vertical angle. Psychology classes mention him a lot to explain how we figured out what the frontal lobe does based on how his apparently ceased it's functions, being severed and all. They don't usually give details about how bits of brain fell out of his head later while he was vomiting but hey, they teach this stuff to little kids.
Realistically I expect he'd have bled out in earlier eras and even so he got some kind of nasty infection that probably had a big chance of killing him.
In particular though I'd like to know any details about what the rod did to th bones it went through. I don't know the anatomy of the skull well enough to tell how much bone it went through at the bottom and can't begin to make predictions about how much damage bits of bone would have caused but I can see the top of the skull having not done much damage if there was no way to reverse the direction of force.
Prior to 1928, any sort of infection would cause you some major problems, wherever in the body it was--obviously you would not be able to treat a brain infection bad enough that amputation would normally be the only recourse. As far as risk of infection, breaching the compartments of the brain is not nearly as dangerous as breaching the compartments of your gut, which are often sloshing with raw sewage.
There's something I can't quite recall about immune response in the brain. It's definitely different than the rest of the body (immuno-privileged might be the word) as microglia put on a bunch of the defensive hats worn by other cells of the body. Inflammation and associated damage might work a bit differently in brain tissue than in the rest of the body, is the short version.
As far as bleeding out, there are worse places to have a tamping rod shot through than your head. If dwarves have technology short of tourniquets to treat any sort of bleeding, and depending on the extent to which brain vasculature is compromised (don't I sound science-y, now?), there's no reason to think that a brain wound is going to bleed out any faster than, say, a spurting femoral artery wound.
Bone shards . . . I don't know. I think a lot of it depends on where the wound occurs. In the Gage example, I don't know that little bits of shattered sphenoid are going to cause more problems passing through the frontal lobe than the whole freakin' (added for emphasis--this was a big piece of metal!) tamping rod.