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 sticky notes then  Notezilla  will show the notification. Go to  Notezilla  Notes Browser, click on 'Unread' filter and make sure you read all the sticky notes (click inside each sticky note to mark it as read). Once you read all the sticky notes, then the new incoming sticky notes will be stuck to Windows desktop.