Is Time Machine sufficient in the case of a reformat? I installed OS X Server 4.0 on top of Yosemite and my VPN got hosed.  I've tried many things to fix the issue including attempted uninstall of OS X Server. Now I am going to re-install the OS.  In preparation for said install, I setup time machine for the first time.  

Will time machine be able to restore files after a OS re-install or do I need to consider manually backing up files?  Second, will time machine restore the potentially broken part of my OS as well (considering I ran time machine after the fact)?
Time Machine will be able to restore all files.
Depending on what you want to restore, you may restore the whole partition or only single files or folders.
Setting up Time Machine you may choose which folders or files to exclude from the backup.


Here is an example of the Time Machine UI:



You may navigate with the Time Machine.app in your Time Machine backup similar like the Finder does on your Mac. You have a third dimension representing time though. If you click on the up arrow you'll move backwards in time. This is also indicated on the time scale on the bottom right side.

If you now want to restore just the blue Adobe folder highlight it and click "Restore" and it will be copied to your main volume overwriting any previous file/folder there.