Hiram Johnson would have become president on Harding's death had he accepted the GOP vice-presidential nomination in 1920. (I am assuming Harding dies on schedule; if anything, having a vice-president as cantankerous as Johnson would probably accelerate Harding's death...) However, it's really hard for me to see Johnson accepting. For his OTL reaction, see David Pietrusza,
1920: The Year of Six Presidents, pp. 237-8:
"Hiram Johnson took it [defeat for the presidential nomination] less well [than Leonard Wood]; but then again, Hiram Johnson probably would have taken victory with ill grace. With his wife and son and secretary, he sat sulking in his Hotel Blackstone rooms. Popular poet James J. "Jimmy" Montague, a close Johnson friend, phoned Irvin Cobb and Ring Lardner: "Come along down to the Blackstone, we're going to sit shivah with the Johnsons. They need company."
"The gloom was intense, and someone opened a bottle of scotch. The phone rang. Johnson's secretary answered. It was Teddy Roosevelt Jr. Johnson knew he was calling to persuade Johnson about the vice-presidency. Everyone in Johnson's suite knew that that would be the only reason Roosevelt would call.
""Tell him I'm not swapping idle conversation with anybody this evening," Johnson fumed. "Tell him I've gone to bed-—tell him anything."
""Hiram," Johnson's wife urged, "for his father's sake if for no other reason, you must listen to him. And he's a fine boy and I'm fond of him. So are you." "This is no time for sentiment," Johnson spat out. "I'm more in a mood for murdering a few people."
"He took the call. “Hello, hello. . . . Johnson speaking. . . . No . . . no, not in a million years. . . . No, I tell you, no. . . . Oh, yes. . . . No, sirree. . . . For the last time, damn it to hell, NO!" Then, face reddened by rage more than Scotch, he hung up--hard.
"Montague had a question. “Senator, there wasn't any doubt as to what you meant by all those 'noes,'” he asked, “But that solitary 'yes' in the middle of 'em-—just here in the bosom of the family, would you mind telling us why you stuck in that lone 'yes'?”
"“Oh, that?” Johnson responded, his mood finally lightening. “That was when the young man asked me if I was sure I heard what he was saying.”"
https://books.google.com/books?id=Uia4A04q8dMC&pg=PT225
https://books.google.com/books?id=Uia4A04q8dMC&pg=PT226
Also, is it sure the convention would even accept Johnson? Even apart from die-hards who couldn't forgive his bolt in 1912, a lot of Republicans--fairly or unfairly--blamed him for Hughes' defeat in California (and therefore in the Electoral College) in 1916.
https://www.jstor.org/stable/25121461?seq=1#metadata_info_tab_contents The fact that his ally Borah had launched a Senate investigation of campaign finances that proved embarrassing to both Wood and Lowden also helped to make Johnson unpopular with the delegates. The convention might have rejected him as it did Lenroot.
On second thought, though: If Harding made it clear to the convention that he supported Johnson and that he feared he might lose the West without him, there is at least a possibility the convention would go along. (In the case of Lenroot, one reason he lost was that Harding never made clear to the convention that Lenroot was
his choice, not just that of a "Senatorial clique.") Perhaps Johnson was a bit too hard-line on the League, but after all Harding himself during the campaign eventually sounded much like Johnson, saying of Article X, "I do not want to clarify these obligations; I want to turn my back on them. It is not interpretation but rejection that I am seeking."
So the Harding-Johnson ticket is of course overwhelmingly elected in November, and Harding dies on schedule in 1923. So Johnson is now President--but the question is, Can he get the nomination for a full term in 1924? The Old Guard will still hate his progressivism, but can they afford to dump a President who is presumably popular in the West, where La Follette was threatening to cut into the Republican vote? If dumped, might Johnson himself rather than La Follette lead a third party? As incumbent President he would presumably win a lot more votes...
Anyway, let's say that Johnson through a mixture of patronage (control of Southern delegates), threats to run as a third party candidate, and some tempering of his earlier radicalism, does get nominated in 1924 and wins? Presumably in his first full term he will be more open than Coolidge to proposals for farm relief, not all of them good. (The McNary-Haugen bill, which Coolidge vetoed and Johnson supported, was probably a bad idea; economists agreed that it would encourage overproduction.) Will he run again in 1928, and if he wins then, how will his handling of the Depression be different from Hoover's? One interesting fact is that as Senator he broke with several of his progressive colleagues to vote for Smoot-Hawley, as he had earlier voted for Fordney-McCumber; he was especially zealous, as one might expect, in getting protection for California farm products.