After yum update is it a good idea to restart the server?

You don't have to restart the server unless you are getting a message (from yum) that explicitly encourages you to do so.

But you can't use the new kernel that was updated until you restart the system (unless you are using something like Ksplice, which is a technology that switches the old kernel with the new one without the need for a reboot).

So in the end, it's your decision if you want to reboot. I would suggest that unless there's a major security update for the kernel you shouldn't reboot during work hours. Otherwise, if the server is idle (and you don't need it for the next 30 minutes or so, because in some rare circumstances updates could interfere with the boot process), I would suggest you reboot it.

If kernel has updated, yes it is a good idea to reboot because new kernel will be used only after reboot. other packages will be updated in place, no need to reboot.

I have a fully automated server that gets its daily updates via yum-cron and I let it reboot every weekend (via root-crontab).

This has been working well for more than three years now.