If anything, to me, "convicted criminal winning an election by majority vote" strongly pattern-matches "effective check against autocracy". Again: look at what the OP is, what fact patterns we're discussing in this thread!
No it's not. The two concepts are orthogonal, and equating the two is a dangerous fallacy. The first is about how someone gets elected to an office - one of the cornerstones of our society is that leaders are elected by the people. The second is what someone in an office can legally do once they are there - another cornerstone is that nobody is above the rule of law. Equating the two effectively throws out the latter.
The distinction is very clear when it comes to a narrowly-scoped office, or even a general executive at a low level like the mayor of a city. It only gets fuzzier as you go up in scale, as those charged with enforcing the law are better poised to not enforce against themselves. But the proper term for that is "corruption".
Sure, and the question of the legality of a given action can also be on the ballot. Implying that someone who wins an election should automatically get out of jail is nonsense. One of the pillars of the bureaucratic rule of law is making it so that no individual has autocratic power. We already have too much of powerful politicians and other agents of the state being effectively above the law.