Passing global variables to alter hooks
The problem is not the global variable, but the fact you are using a function like drupal_set_message() inside a alter hook, which is not necessarily invoked when Drupal is outputting a page.
If you want to debug a hook, it's better you go with watchdog() and check in admin/reports/dblog if there is any message. You need to enable the Database Logging or the Syslog module to see any output; in the latter case, you will see the output on the syslog of your computer, instead of admin/reports/dblog.