Yes. J. Reuben Clark was a high-ranking Mormon during WWII time...and he was quite an outspoken pacifist who obviously influenced many Mormons of his generation, who in turn passed it down.
I'm not sure how Mormons faired in serving in WWI -- but certainly they were represented.
And then there was George Romney (Cousin to Marion Romney, mormon apostle and a member of the first presidency)
He was Gov of Michigan and went with some other governors to Vietnam in 1965 and came back saying he supported the operation there.
Neither he nor any other gov developed any illness and they werte all for the war.
However later, when his son Mitt was about to be drafted George suddenly remembered that the visit caused him a nervous condition and that he had been “brainwashed” ...and as Gov he was in charge of the state draft board.
Due to George Romneys efforts Mormon boys in Michigan and Utah had deferments handed to them like candy...if they got a draft notice they were quickly deferred and sent on a “mission”
Georges own boy, Mitt, was drafted twice and dodged both times with the help of Big Daddy Geotge ...the first time Junior was sent to a cosy assignmernt in Paris for 2 1/2 years, living in a mansion and driving a Citreon...the 2nd time George packed him off to college...
Many mormon boys were “deferred” and dodged the draft during Nam...
Baptist boys...not so much...
No Romney has ever served in the US military...
In my SEVEN years in the US military during Nam I never met a mormon...
Years later, in 1877, I met one female mormon, who had just joined and she spent more time prostlysizing amongst the enlisted women that she did bothering about duty...