If anything, getting into Harvard Law after graduating from Whittier College might just increase the resentment RMN felt for the 'eastern elite'. He's still a relatively poor guy (if hardly destitute), and now he's surrounded by many more affluent WASPs than he would be at Chapel Hill, North Carolina.
But, strangely, he may never apply the qualilfier 'liberal' to the 'eastern elite' tag, as he would come into contact with a whole lot of raw anti-New Deal opinion from the wealthy students in the year of the court packing scandal. In OTL it was upper middle class liberals in the post-war DC public service like Acheson, Harriman, and most notoriously, Alger Hiss, that shaped his vision of just who his enemy was.
I don't know why postgrad Nixon would meet undergrad JFK, though.