I'd also like to note that even if we posit a wildly, amazingly successful career for Jackson, that won't be enough unless there's also been a massive swing of opinion in the Tory party room, among people who have been in Parliament for literally decades.
Look at Joseph Chamberlain: he moved to Parliament after a wildly successful career in local government as a reforming mayor of Birmingham, as well as industry- Jackson was a cricket player. Chamberlain had personal connections and friendships with reforming circles not just in Britain but across the Dominions- Jackson did not. Through Chamberlain's widespread popularity among the base of the party and his role as leader of the radicals, he became President of the Board of Trade- a cabinet position!- after four years on the back benches. Jackson, a man who was respected but not seen as charismatic nor with any history of wide appeal to the party, made it to a junior ministerial post in the War Ministry (not cabinet) after seven years, and did not distinguish himself. Chamberlain broke with Gladstone, built a core of Liberal Unionist around him, shattered his party and emerged as a powerful third force in British politics- Jackson resigned having never reached higher than that one, brief spell as a junior minister.
I'll stop the comparison there because that's just what Chamberlain did in eleven years- the time Jackson was in Parliament. You'll note everything I left out- the time he spent building up the Unionists following the party break, the battle to get funding and set up branches, the deal with his old rival Salisbury, the time at the Colonial Office, breaking with his new allies. All that took another twenty years of hard work, and it was unsuccessful.
And that's worth hammering home- after thirty years in Parliament, with skills and resources no one had had, with ambition and a clear program of reform and a literal world-wide network of allies, Chamberlain did not get his reforms passed. He is, at the end of the day, a might-have-been. And that's in large part because again and again and again it was proven that public popularity- and there were times when Chamberlain was very popular with the public- does not mean anything without a majority of parliament. Not only did Chamberlain never get that, he never, at any point came close to getting the majority of people on his side of parliament.
I simply don't buy that a non-entity of a Junior minister could somehow be more successful in a third of the time with none of the advantages in a party that was even more hostile to Home Rule than the Liberals or Liberal Unionists after all the Home Rule crises of the past few decades, the Tory elites literally staking their careers on a civil war rather than making concessions to Home Rule, after a war that the IPP supported on the basis that they would be awarded their seats at the end of it.*Even if he kept his mouth shut about Unionism- not really possible, but alright- and even if he was vastly more successful as a junior minister than he was in our timeline... that doesn't change the fact that he couldn't have got to Cabinet or come even close to being a leadership candidate.
*That's another thing- how on earth has the IPP lost thirty seats if Sinn Fein isn't there to pick them up?