I am currently putting on my flame proof suit and eye protection for the responses
But YES, a properly loaded .38 special in the right place will Kill a whitetail !!!
But ...my experience with this is limited to a model 92 rifle, Not a handgun.
A 180 grain lead semi-wadcutter actually penetrates pretty well from a rifle.
I gained access to a tract of hunting land several years ago that is kind of small
and very thick cover. problem was, I did not really want to draw a lot of attention to myself
when I shot so I worked up a load for my .357 rifle with .38 cases and went to work with it. ( I was legal to be there, not poaching or anything. Just some "EVIL" neighbors)
It did what I wanted it to do. keep in mind that ranges were extremely short.
In all honesty, I would not try it with a .38 handgun though.