Did World War II happen?
There is some evidence that a World War II happened.
Lex says in Batman vs. Superman...
"You know, dad was born in East Germany. He grew up...eating stale crackers. And every other Saturday, he had to march in a parade and waved flowers at tyrants. So I think it was providence that his son, me, would end up with this. "
East Germany only came into being as a direct result of WWII.
Did Wonder Woman fight in WWII?
Based only on the movies to date (10/2017)...we don't know.
It seems likely that, if she did, then it was on a very low-key level since no-one recognises her.
The implication of what we know is that Diana slips into the shadows of history and if indeed she took any action during WWII, Korea or Vietnam etc. it hasn't been public knowledge since no-one is aware of her.
Certainly in BvS she says..*
A hundred years ago I walked away from mankind. From a century of horrors. Man made a world where standing together is impossible.
The implication is that she did NOT take part.....but that may get retconned in a later movie.
* Hat-tip to this question/answer at SF&F