To answer your question, if you have a WSUS server you should be able to tweak the WSUS settings in Group Policy to automatically reboot if required. If not, you should be able to set Windows to automatically reboot at the specified time (it's in the configure Windows Updates dialog).
This next part is not quite answering your question, but I think it's important that you bear it in mind.
Personally, I always do my Windows Updates on a weekend and am always physically present on site when installing Windows Updates. As unlikely as a Windows Update is to brick your server, it can happen and I'd quite like to be there if it did crash my server when I rebooted it.
If I'm on site at the time, I know it has gone wrong immediately - if I'm in bed at 5am, I would only find out it crashed when I got up and saw the Nagios alert on my BlackBerry. If you are on site when it goes wrong, you have a massive advantage in that it's the weekend, so you have some breathing space to fix the problem. If you've ever walked into your office at 9am and a server is down, you will know it isn't a fun experience.