Is it possible to execute an external application from a trigger?

Yes this is possible, you can use the following script to do this:

Dim WshShell
set WshShell = CreateObject ("wscript.Shell")
WshShell.Run "path to your application goes here", 3 

If this application has to interact with the desktop (i.e. it has a GUI) you have to enable this.

To do this, go to the ‘Control Panel’=>’Administrative Tools’=>’Services’ and double click the SMS messaging server service. Select the ‘Log On’ tab, and select the ‘Allow service to interact with the desktop option’.