Can I Run custom callback in site maitenance mode
If you want to test few menu item when Drupal site is in maintenance mode. You can use Maintenance Exempt module.
From this module's page:

Drupal allows you to set your site into maintenance mode in order to deploy code and database upgrades safely. However, access to the site during maintenance mode is by default controlled by a permission, which is generally only given to administrative users. It's not possible to test the site as a regular anonymous or authenticated user without giving all anonymous/authenticated users the &quot;Use the site in maintenance mode&quot; permission, so you generally have to test those things on the fly after moving the site back to &quot;live&quot; mode.
Until now, that is! This D7+ module (the necessary hook doesn't exist in D6 and below) allows specific people to perform the necessary testing on the site with all role combinations without opening the site up to all of your visitors.