Does a new site installation run through hook_updates of every module?
When you install a module, the largest number found in hook_update_N hook will be stored in the system table's schema_version field. It will not run the function. Just stored in the table. 

When you copy a module to a new site, any of the hook_update_N hooks will not be executed for you. However, if you would like to make any change, you can implement hook_install to make the necessary database or any other changes.