The answer is no.
The basis and focus of modern Leftism (although this was not always the case) is the mass media - and universities have a very secondary role.
Universities and colleges do not (to any significant or important degree) train the intellectual elite in political correctness, for the simple reason that modern universities (with a few exceptions outlined below) do not train anybody in anything.
To train somebody means to teach them a skill. To learn a skill means to be able to do something you could not do before.
To develop skills requires multiple repetitions (practice) under supervision (eg. learning a musical instrument, learning to dance, learning a sport).
By this criteria modern universities do not develop skills at all.
(Except in the minority of professional schools such as medicine, dentistry, law, engineering and the like - where there is a significant element of skill training by repetition and rote, as well as transmission of knowledge and attitudes.)
In fact (with the exception of the above examples) British universities have never had much to do with developing skills.
Before they were corrupted into futility, they relied upon skills already inculcated at school; and were mostly focused on providing information/ knowledge relevant to the future career.
(Non-professional degrees were mostly for preparing grammar school/ public school teachers; thus a History degree would provide the information needed to be a history teacher, and so on. Before this time, the classics degree was a necessary preparation for being a priest/ gentleman.)
And Britain (with a bit of help from France) pretty much invented Leftism, and dominated international Leftism up until the post-1945 era.
I don't think universities ever had much to do with generating the ideas of the Left - these were mostly developed outside the academy (or on its fringes) by freelance intellectuals and creative writers - at a time when the universities were repositories of conservative, traditional values.
Rather, universities were simply drawn along behind the Left, secondary to dependence on State funding, subsidy, regulation; and always lagging the cutting edge.
Universities have, nonetheless, done a very useful job for the Left by validating politically correct ideas with pseudo-scholarship, adding prestige and authority to what would otherwise have been recognized as obvious nonsense and wickedness, and by declaring inconvenient truths and hate facts to be 'unscientific', 'nonsense', 'not peer reviewed', 'evil ideas funded by evil people' and so on.
But this is not the generative and power focus of modern Leftism: that would be the mass media.
It is the mass media which disciplines and punishes the academy and the academics for ideological transgression; not the other way around.