Mebbe.
Mebbe not.
When I was at Seneca Army Depot, there were lots of trophy-size deer there, all white.
That was the result of the government fencing in the entire reservation many, many years ago.
My memory of the historical facts of the Depot may be a little off, I seem to remember it was around the WWII era or before that they fenced it in...but anyway, it didn't seem to affect the deer.
I attended several check-station weigh-ins and found all the deer to be in good health, relatively free of disease and very few ticks, fleas, etc.
The herd was also managed - lots of food plots, winter feeding, etc, and hunting was pretty much restricted.
I was on a "I wannabe a wild game biologist kick", back then.
I got over that, but I still know how to check deer for age, body fat, disease, etc.
I've seen much, much worse in so-called "wild" deer herds in AL, GA, FL and MS.