Notezilla does have an option to stick the Windows sticky note directly to the desktop.
Right click on Notezilla icon, choose Preferences, go to Advanced tab and enable 'Stick incoming notes directly to desktop', also 'Stay on top' option if required.
Now all sticky notes that are sent to this computer will appear on desktop.
However, If there are multiple unread notes then Notezilla will show the notification. Go to Notezilla Notes Browser, click on 'Unread' filter and make sure you read all the notes (click inside each sticky note to mark it as read). Once you read all the notes, then the new incoming notes will be stuck to desktop.