Anna Chennault, 1969..
Yes he did act, but fairly late in the day. We can never know if it had real bearing on the war and its outcome. I suspect that it did not simply because the South could make the same calculations and hoped for a better friend than Johnson.
At the time both sides were hanging on having mauled each other through the Tet offensive. The Tet offensive while providing a dramatic propaganda victory to the North had actually destroyed the bulk of long husbanded military assets in the south and these were never ever replaced. This forced the North to adopt a strategy of waiting for the USA to actually leave before unleashing regular army forces to then conquer the south in 1975.
There is good reason to think that the North would have been willing to enter a peace arrangement in order to allow rebuilding and the get the USA out. This is something that could have been done by Johnson to leave the incoming administration blameless for the collapse of the South as well.
In the end we slipped into a protracted arm wrestle that still led to US withdrawal.
Whatever difference it might have made, it secured the presidency for Nixon as probable as that was in the time and place. Yet this action was treason and really bad judgement. That same flawed judgement led to Watergate.
Nixon’s Vietnam Treachery