Is it possible to have new pages automatically added to the primary menu via functions.php?
This particular theme will be deployed on a special version of multisite, so the checkbox which is available via admin isn’t an option.
I can’t seem to find anything in codex or on here.
Not a specific answer, but will be too long for a comment. You could also try looking at the code that WordPress core uses itself. I know you said you couldn’t use the check box that auto-adds pages, but you could look over how it is being used. A little digging around (with a decent text editor you should be able to search for a phrase throughout the entire WordPress code base) in the WordPress code reveals:
This code is run on:
Maybe this will point you in the right direction and perhaps you can copy what WP is doing to do something similar.