For this test you will need two users.
As your primary user in your messaging settings make sure you are configured to receive popups for personal messages and that "Beep when popup notification is displayed" is ticked.
As your second user send your primary user a personal message.
Check that the primary user's popup is accompanied by a notification sound. You can go and play the sound in message/bell.wav to see what it sounds like.
Untick "Beep when popup notification is displayed".
Send another message to your primary user.
Wait at least 2 minutes (at least 2 minutes is required between popups to avoid annoying people). Check that the primary user gets their popup without a notification sound.
Note that this will probably not work on a computer without Quicktime installed if you are using Safari.