Some do. Many don’t. Most of the Mormons I knew in the military were either converts while in the military or ‘jack mormons’ not active ones. A big part of this is because the average age of joining the Military is 18-22 and active Mormon men are expected to serve an LDS mission from the ages of 19-21.
I have yet to personally meet a Mormon who joined the military after serving his LDS mission. However, I have pinged an ex-mo who might have some insight and 2 never Mormons who were in the Air Force for many years.
My experience as well. I think it is telling given that this country was not founded on mormonism. I'm sure there have been mormons that have served, but I doubt the ratio even compares on an equivalent basis to the descendants of Christian founders of this once great country.
The only one I ever met I (and I’m retired) was a thoroughly Jack Mormon. He was the one I first heard about the magic underwear from. After I was aware of it, I noticed the tell-tale “pantie lines” across the thighs of several male acquaintences over the years, but that was it. Never heard of a Mormon female in the military.