To recycle an old post of mine:
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Kornilov's own appraisal of what would happen doesn't sound entirely cheerful:
"Kerensky warned him of the dangers of a military dictatorship, which would have to contend with a general strike and a massacre of officers. Kronilov was not intimidated: "I foresee that possibility, but at least those who are left alive will have the soldiers in hand."
https://books.google.com/books?id=fOxopOa4ogUC&pg=PA250
But even that was IMO too "optimistic." Kornilov was definitely for continuing the War: "The Provisional Government, under the pressure of the Bolshevik majority in the Soviets, acts in full agreement with the plans of the German General Staff . . . I cannot betray Russia into the hands of its historic enemy, the German tribe, and make the Russian people slaves of the Germans."
https://books.google.com/books?id=kdQFBAAAQBAJ&pg=PA107 I just don't see the ordinary soldiers, sick of the war, worked on by socialist agitators, anxious to go home and seize the landowners' land, following Kornilov. It was too late to re-establish military discipline six months after Order No. 1.
https://en.wikipedia.org/wiki/Petrograd_Soviet_Order_No._1
There is incidentally some dispute as to whether Kornilov originally intended a "coup" or whether he believed that he had Kerensky's support, and that if Kerensky got cold feet at the last minute, it was only because he was a captive of the soviets. But I don't think that matters--with or without Kerensky's support, Kornilov could not succeed.
Brusilov's characterization of Kornilov as a "man with the heart of a lion and the brains of a lamb" was not really fair, but all the same, people who see Kornilov as a potential saviour of Russia from the Bolsheviks do IMO overrate the man and his prospects.