When I log in after every OS X update, I get a push notification saying that my computer is being optimized and that performance and battery life may be affected until it's complete. Is it dangerous to restart my computer again immediately after getting this notification? (I have to reboot in order to make my manual Continuity activation work.) And if so, how can I tell when the process is done?
No, it is not dangerous. Pretty much every single task is queued and persisted if needed. Unless you have a foreground task that has a nice "x" button to stop it, you can reboot, shut down, sleep etc. with no trouble at all. System tasks in OS X are designed to be fully automatic, autonomous and out of the way for the user.
When it is complete you might get another message from the notification center, but it will probably just silently be done and your system will 'feel' much faster.
Most of the post-install optimisations are things like Spotlight indexing and LSServices doing it's thing.
If you want to see if your system is doing something in the background, you can open up activity monitor and leave it idle for a bit so OS X detects that you aren't doing anything and then takes a little bite more CPU power and memory to do system tasks until you come in and start doing things again. You will probably see processes like "mds" using a significant portion of your CPU time. It is part of spotlight and collects information on where everything is so you can use the search function to find your stuff.