I have not used mine for field dressing deer, but I believe you would probably need to pause several times to touch up the blade. However, I can say that while the mild steel blade dulls quickly, it also sharpens easily. A few licks with a file and you're good to go again.
You can get a mild steel blade quite sharp. It will cut. It will not dull immediately, if you use it properly, but it will dull faster than a knife made of harder steel and will therefore require more frequent sharpening, and over time will wear out faster than a knife of better steel due to repeated sharpening. However, it will get the job done.
I'm pondering that phrase, "...before the edge gives out." I don't know if that means the point at which the knife begins to dull, and needs "touching up," or if we mean the point at which the knife gets so dull it will not cut, and requires a major sharpening session. Many people take great pride in keeping their cutting tools sharp, but a surprising number of folks would rather work with dull tools than go to the trouble of sharpening them.
Many years ago, I did a lot of work with fresh, green hides, mostly deer and cow. I used a Green River Dadley blade for fleshing, trimming, and scraping off the hair. I think these blades are made of 1075, with Rc hardness in the mid fifties, but I'm not certain of that. The knife worked best when it was sharp. I started every session of hide work by whetting the knife on an India stone to a near razor edge. I kept a Schrade HoneSteel in my hip pocket and would pause and steel the knife every few minutes. Steeling the blade took literally seconds. This sounds tedious, but in fact it made the work go faster by keeping the blade sharp, and I was usually ready to straighten up from the fleshing beam and rest my back at those intervals, anyway.
The best way to answer the question to your own satisfaction might be to make (or have made) a knife of mild steel and try it out. Chances are pretty good you will not be happy with it if you are used to working with knives of modern high-carbon steel with proper heat treatment, and you'll think it is a lousy knife. It's just that the common folk on the frontier two centuries ago would have not had that frame of reference. They might have only been familiar with the "soft steel" knives as described in the literature of the period... They would not have known any better, and would have done the best they could with what they had.
Best regards,
Notchy Bob