Yes it is possible.
Install the Play 2.x plugin (with dependencies) and add a launch configuration designed for Play 2 ( note in Intellij 14 Play2 support integrated in Scala plugin )
Menu > Run > Change Configurations ... > Add New Configuration (plus icon in the corner)> Play 2 App
After saving, you can start the application (also in debug mode) inside IntelliJ - that is, through
Menu > Run > Debug 'Your Project'
btw, you can remove Make (before starting) from there, SBT should correctly handle builds without Idea support
See sample picture

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