Close but slightly different. As I envision it, the random selection would only be for the pool of candidates. People in the pool would have the option but not the obligation to run and there would still be campaigns and voting as there are now, just with a very narrow slice of the population eligible to run if they choose.
The only goal is to remove politics as a career option, since it is quite improbable that any one person would win the lottery to be eligible. A secondary goal is that a potentially great leader who would not have considered politics under current system’s may well be called to duty if they are drawn into the pool and view themselves as a strong option within the pool.