I clicked to automatically disable a problematic add-in in Microsoft Office 2013 (Word, Excel) and I was unable to force Word to enable this plugin at start-up. I had to change a registry key:
For 32-bit: Root\Software\Microsoft\Office\application name\Addins\add-in ID
For 64-bit: Root\Software\Wow6432Node\Microsoft\Office\application name\Addins\add-in ID
Where Root is HKEY_CURRENT_USER or HKEY_LOCAL_MACHINE.
Change load_behavior from 0 to 3. The add-in will than start automatically.