Yes, you can customize the locale. Here is an example I did in the User Profile:

You can make a similar change on the System Locales screen for a site-wide change. 

On the System Locales page you can update the date and time formats.  Using the “HH” indicator for hours will give you a 24 hour clock.  You’ll likely want to update all the Date/Time options so they’re all consistent throughout the system.  Then press Close on the pop-up window and Save on the System Locale Pages.  Refreshing your screen should update the settings in the header