He would have done way better than McGovern, but I doubt that anyone could have beaten Nixon in 1972 under the real life conditions. RFK might have picked Carter for VP, though that doesn't make him competative in the south. I gave him GA in the scenario, but I'm even doubtful about that.
✓ President Richard Nixon (R-CA)/Vice President Spiro Agnew (R-MD): 405 EVs.; 55.4%
Senator Robert Kennedy (D-NY)/Governor Jimmy Carter (D-GA): 133 EVs.; 43.6%
Seems about right, though I would also flip Wisconsin, Oregon, and Connecticut to Kennedy.