Well, lemme get one thing out of the way first: There was more to ancient medicine than most people realize. (I'll give you an example if you like, but suffice it to say, they were a hell of a lot smarter -- and in some cases, a hell of a lot dumber -- than you might think.)
Following that up, yes, it's absolutely possible to survive ... and Briar is fairly on track with the details. Obviously, if you slice through specific areas on the body properly, you're going to die instantly at best and an agonizingly painful, unavoidable, slow death at worst-- which is true of modern day, too, you understand. Stabbing a person in the right spot is the same as shooting them in the right spot. There are just some injuries modern medicine cannot fix.
Best case scenario? Get run through with a relatively small (by width and thickness, not length) blade, get it out quickly (while hoping to God it's not poison-covered or barbed in some way), stop the bleeding promptly, wrap it up, and keep the wound and dressing pressed against it as clean as possible. "Amount of trauma" and "to what" is your biggest issue, followed closely by loss of blood and how much, and rather distantly by cleanliness, because ... being perfectly honest, being more 'hardcore' then meant that people could handle some extra germs. Women have been giving birth in the dirt for millennia, several successful surgeries were performed in incredibly nasty environments, and depending on the era, people were already competent in the concept of cleaning war wounds. :P Actually, on that note, ever see Gladiator?
