Yes. Really.
It was Paul VI's "day of peace" idiocy that got LBJ to call the cease fire after He'd virtually bombed the VC into oblivion. Paul VI was convinced that the VC was ready to talk surrender and he exerted as much influence as he could on LBJ to stop the bombings. That allowed the
VC to rearm and the subsequent Tet offensive was the beginning of the end for the U.S.
Don't get me wrong, there is plenty of idiocy to go around LBJ, MacNamara, the hippies, Kennedy etc. But a Pope being among them and contributing to the detriment at a critical juncture is tragic.
As you recall, the NVA/VC actually LOST the Tet offensive. The decision to lose the war was political (LBJ's)--not a result of Paul VI's intervention.
And when I say 'political,' I mean it--LBJ made the decision politically. He may have been influenced by any one of hundreds of factors, but none of them were based on sound military judgment.
Your thesis is absolutely improbable.