Some or all of this might be wrong, however my understanding is that Gage was able to speak within _minutes_ (not _seconds_) of his injury, and walk with a little help to the cart, where he sat until he was able to vomit a bit of brain out in front of a (presumably either horrified or intensely interested) physician.
He was then very ill for months afterwards, barely mumbling his responses to people. This was with the best care available at the time.
Imagining that his injury were caused by a Dragon rather than a crowbar (or whatever it was the tool was, some kind of iron bar for poking at explosives with I believe), I don't think he could have continued the fight.
If there are cases that show someone fighting with a torn brain, I'm definitely extremely interested in them!
Seeing a dwarf fight with a torn brain isn't unrealistic.