> Corruption makes things more democratic in an autocracy...

Technically, maybe yes? But autocrats tend to use "de facto authorized" corruption as a carrot for their loyal supporters, and "arrested for corruption" as the corresponding stick. Which leads to outcomes little different from an absolute dictatorship.

Except the autocrat now has a convenient scapegoat for problems affecting the populace - corrupt officials - and a nice narrative for explaining the sudden removals of officials whose loyalties or performance were not to the autocrat's liking.