No, ROS doesn’t reboot automatically, you’ll have to do it manually. Or not, with mature devices routerboot firmware mostly doesn’t change at all between ROS versions so there’s no need for immediate reboot. When device reboots next time, it’ll run updated routerboot as well. If you run into some troubles, you may want to reboot device manually, possibly power-cycling it as well (to make sure all components get a clean start).
I have a device which upgraded routerboot (actually I did it manually) from 6.47.1 to 6.47.7 … but with 11w3d uptime it’s still waiting to get loaded… I’ve obviously no issues with the device. It could well be that it’ll get loaded when I decide to upgrade ROS to 6.48.2 (or whichever version I declare stable enough).