I've got a Gulp workflow that I'd like to automatically launch upon opening my project in PHPStorm. Is this possible?
Not possible at the moment.
https://youtrack.jetbrains.com/issue/WEB-11818 -- watch this and related tickets (star/vote/comment) to get notified on progress.
UPDATE: This functionality is now implemented and available since PhpStorm v10 / WebStorm v11 -- look for it under Settings/Preferences | Tools | Startup Tasks.
This allows you to execute any existing (or create new) Run/Debug Configurations on project opening. This includes Gulp/Grunt tasks as they can be invoked via Run/Debug Configurations functionality.