I believe you may be able to use the onComplete event of the SSJS to notify a user as well.
Typically, you would set the value of a hidden input field to the value of the alert content with the SSJS, and then simply grab that value (typically innerHTML) with the CSJS and use it in your alert statement.
You'll find the onComplete event in All Properties when you have the SSJS selected in the Source pane (well, that's how I find it anyway!).