Certainly, and I imagine that there are plenty that we interact with on a regular basis. For example, door security sensors (like for Ring) will be off nearly all the time. When someone opens the door, they will power up, send a notification, and go dormant again. I don't know if this will happen within a single millisecond, but it certainly could if there was a design need.

For many simple embedded systems that plug into the wall, the "boot" process will happen in under a millisecond. But it will take considerably longer than that for the voltage levels to stabilize.

The real thing which differentiates these from a PC or phone is that they are not running what we would typically call an OS. They may be running an RTOS (a very simplified OS), but for many of them, as soon as they have stable power, they are off to the races (Just like the home-computers of the 80s. Just plug in and go.)