I'm not at all convinced Vietnam wouldn't have been just as messy and tragic with JFK in office. After all, he put us there in the first place. No president wanted to go down in history as the first to admit failure and defeat in a high-profile contest against Communism, and JFK already had the humiliation of the Bay of Pigs to live down. I'm confident he'd have been as hamstrung by the "too deep in to give up now" mentality as anyone in the office.
Kennedy escalated our involvement, but Ike had around 900 advisors on the ground in the South after the French turned tail and ran.
You'll note in the review DBN links to, the Vietnam conflict isn't treated any differently than any other war. If not for the year in the indicia (1969), the story could have taken place in Korea or Japan just as easily. That we're still in it in '69, and in apparently large numbers, shows there was an "escalation," but there's no suggestion of "suffering and upset" stateside. Indeed, the war seems pretty much "out of sight, out of mind" for our cast of characters until Clark gets some letters from servicemen this one time, unlike WWII which drove all manner of comic-world references to spies, saboteurs, fifth columnists, quislings, shortages, paper drives, war bonds, etc. In 40s comics, you never forgot there was a war on, but in 60s superhero comics, you could easily miss the fact that the US was in 'Nam at all. But then there is this story, and the JLA tale spotlighting a returning Marine, and so on, so we know it did happen, just presumably in a tidier and less controversial fashion. The Marvelverse got Oliver Stone's "Platoon" version of 'Nam, and DC got John Wayne's "Green Berets" version.
Were the War comics DC published in the same era considered to be part of the DC Universe at large? Our Fighting Forces featured US Army Captain Phil Hunter on the ground in Viet Nam trying to save his brother from a Viet Cong P.O.W. camp. This comic was published in 1966.