Yeah, what you described is how I understand it's supposed to be done.
I'm pretty sure you don't have to aerate, but I haven't actually done this before so I might be wrong. The yeast use oxygen to multiply and then when the oxygen runs out, they start producing alcohol. So if you already have a cake that's got a big enough yeast population to do your fermentation, the yeast can just skip the oxygen-consuming phase and get right to making alcohol.
You don't need to stir, and I don't think disturbing the yeast bed will hurt either. There is a video floating around that's a time lapse of a carboy where fresh wort was pitched onto a cake. Over the course of a few hours, the yeast cake literally wakes up, rises up into the solution, and sets up camp at the top of the carboy to form a new kreuzen, without any encouragment other than having fresh wort dropped onto it.