A possibility like that: who knows?
I suppose we might ask what alternative course might have followed without Kennedy's decision to seek a formal Congressional approval for military action following the attacks on the destroyers in the Gulf of Tonkin in the summer of 1964. Though Johnson publicly supported the resolution at the time, Johnson's advisors always complained about this maneuver from a lame duck president just months before Johson's general election. We probably wouldn't be faced with as much conspiratorial speculation about that incident if it had been Johnson already serving and not his rival. In any event, that was a fateful commitment and it tied Johnson's hands. Perhaps a President Johnson in the summer of 1964, serving but not elected, might have tried to avoid a congressional resolution? That would be in keeping with what he later said was his greater commitment to domestic legislation. It would have been an opening to avoid all of the draft-related rioting he faced in his actual single term, anyway. There might have been no way around that, though.
I read in a history of the secret service, by the by, that there was an increase in presidential security following the so-called Oswald incident. The author argues this response was probably an overreaction. For all the justified outrage about the victims in the crowd, Oswald was about 90 yards away from the president. He was six stories up in a nearby warehouse. And he would have had time for only one aimed shot, or at most, two. To hit Kennedy in that moving car, much less to hit him fatally, would have required an extraordinary act of marksmanship. Still, it was a response the service welcomed.