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 militaty 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.
There *was* one matter on which Kornilov later (during the Russian Civil War) shpwed some originality, though:
"On one point, however, Kornilov's views departed considerably from the ideals espoused by the White leaders — on the all-important question of Russia's territorial integrity. Not only did Kornilov show readiness to grant broad autonomy to the borderland states even before the convocation of the Constituent Assembly, but he was also willing to recognize the separate political status of Poland,27 Ukraine, and Finland: 'Poland, Ukraine, and Finland, having formed themselves into separate national state entities,' reads article fourteen of [Kornilov's draft] program, 'should be supported by the Russian government in their strivings toward state regeneration in order that in this manner the eternal and indestructible union of the brotherly peoples might grow even stronger.' [That almost sounds like "unbreakable union of free republics" as the later Soviet national anthem would have it...--DT]
"Kornilov's program did not remain a closely guarded secret for long. When rumors regarding its existence reached Alekseev, the old and generally self-composed soldier became so incensed that he angrily demanded to see it immediately. Miliukov, after studying the document, indignantly branded Kornilov an 'adventurist' and 'political dilettante,' and warned Alekseev that if the program was publicized, broad support for the VA [Volunteer Army] would immediately disintegrate.
"Kornilov's program would have constituted a landmark in the evolution of the nationality policy of the White movement and undoubtedly caused a bitter conflict, perhaps even a schism, within the VA, if the events that followed--the costly Kuban campaign and Kornilov's sudden death--had not consigned the document to oblivion..."
https://books.google.com/books?id=irWQQCXwhwwC&pg=PA42
The idea of recognizing Ukrainian nationality on the same level with Polish and Finnish was, for a White--well, let's say, unusual! Most likely, if Kornilov had lived, the attitude of other White leaders would be, "You're a fine general, Lavr Georgiyevich. Stick to that and leave politics to us..."
(BTW, it's not clear whether Kornilov's mother was a Kazakh or an Altai Kalmyk.
https://books.google.com/books?id=wLvaCwAAQBAJ&pg=PA184 Either way, Kornilov liked to dress "exotically", speak in Turkic, etc. But as long as he supported the war, how could he do anything about the immediate cause of the Central Asian Uprising of 1916--the conscription of central Asian Muslims into labor battalions for the Eastern Front?)