If Kornilov launches "coup" with support of Kerensky, then it isn't a coup or military dictatorship, just Russian equivalent of Ebert–Groener pact.
Ebert, even though leftist, was keenly aware that German revolution could spiral out of control, so he came to an agreement with military establishment. That agreement amounted to "military establishment accepts new republican government and constitutional assembly, and government agrees to stop any further revolutionary activity".
There was no evidence that Kornilov wanted to seize power, he just wanted to crush Soviets and end "Dual Power", seemingly at instigation of Kerensky. If Kerensky didn't back off at last moment, Provisional government would gain full control of country.
Ebert allied with right-wing militia to defend french-style republic, whereas Kerensky released and armed those who wanted to replace it with soviet style republic. With "leader" like this at helm, there was no chance that Bolsheviks won't launch their coup.
If Kerensky doesn't backstab Kornilov, Bolsheviks stay in jail, and no further revolution takes place, or at worst is suppressed over week or two, like in Germany. Russian army won't disintegrate if government doesn't purge officer corps in aftermath of Kornilov affair.