Well, if you're on Windows you can schedule Window to run a file
whenever you want. So if that file is a .jsx file, with a #target
InDesign statement (you would need to look up the exact way of targeting
your version of InDesign) it will, I think, open InDesign when it runs,
and run the script.
If that's not possible, you can schedule Windows to run InDesign at your
designated time, and write a startup script in InDesign (that checks
more or less what time of day it is) that will run whenver InDesign opens.
So that's two ways to play with.
As far as I understand the EULAs for InDesign, something like this is not allowed. It’s a fully automated task. You can find the EULAs here (for CS6):
And it says:
220.127.116.11 For clarification and without limitation, the foregoing does not permit Customer to install or access (either directly or through commands, data, or instructions) the Software: (a) from or to a Computer not part of Customer’s Internal Network; (b) for enabling web hosted workgroups or web hosted services available to the public; (c) by any individual or entity to use, download, copy, or otherwise benefit from the functionality of the Software unless licensed to do so by Adobe; (d) as a component of a system, workflow or service accessible by more than the Permitted Number of users; or (e) for operations not initiated by an individual user (e.g., automated server processing).
None of the points (a,b,c,d and e) do apply here!
To awnser the question: create a launch deamon to run the JSX at night.
My understanding of (e) differs from yours: A process automatically launched by a demon is one »not initiated by an individual user«.
But it only was a hint.
1) An individulal user == single user (as distinct from a group of users)
2) The example even clarifies that:
(e.g., automated server processing)
A server is a computer that provides services – such as file services, mail services, or web services – to other computers or network devices.