You can set Notes to announce new messages at an interval you choose, regardless of whether Notes is running.  You can set either a sound or a visible notification and specify a particular sound.

1.  From the menu, choose File - preferences - User Preferences.

2.  Do any of the following:
..... Deselect  "Show a popup" - this will STOP the dialog box showing when you have new message
..... Deselect "Play a sound" - this will STOP the sound option when you have new messges
..... Deselect "Show an icon in System Tray" - this will stop the Notes New Mail icon.  This icon appears in the status are of the Windows taskbar while Notes is running, just after you receive new mail, and disappears as soon as you use your Inbox.