Impossible at the moment.
https://youtrack.jetbrains.com/issue/WEB-11818 - see this and related tickets (star / voice / comment) to receive notification of progress.
UPDATE:. This functionality is now implemented and available since PhpStorm v10 / WebStorm v11 - find it under Settings/Preferences | Tools | Startup Tasks Settings/Preferences | Tools | Startup Tasks Settings/Preferences | Tools | Startup Tasks .
This allows you to run any existing (or create new) Run / Debug Configurations when opening a project. This includes Gulp / Grunt tasks, as they can be called using the Run / Debug Configurations functions.
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