LBJ probably would have dropped out regardless. Kennedy's run may have been what broke the camels back but Johnson could obviously see what was happening and how unpopular he was, and even if it's delayed, I'd say he would have ended up dropping out.
RFK will probably build up his political strength in the Senate, and if Nixon still gets caught in Watergate, may take a swipe at him. After that, I'd say he'd run for the White House in 1976, but how well he could manage things at that point is debatable. The economy is heading for the tank, and would face national malaise were Nixon caught. But, that brings up a larger point. What RFK does or how well he governs relies heavily on what happens around him. There's a big difference between HHH winning and things going from there or Nixon winning and things going on from there, not to mention other candidates who could have won the nomination instead for 1968.