will the kiosk renew my registration the same day as I (of course) pass a smog test? Does the kiosk know that vehicle passed smog test right away?

To be safe, I'd give the system a few hours (up-to 24) to ensure the systems update. You will get a message saying the smog check is still not in the system, so it doesn't hurt to try and come back later if necessary...

Once the smog check has passed it is instantly updated to the California department of motor vehicles mainframe database.