Based on experience, you can deploy 'something' out there and build that 'something' really fast with Grails. GORM instantly takes care of persisting to DB with minimal effort, there's not much to configure. If you're planning to just create an API Server, the latest Grails 2.3.x releases have specifically made that easier too.
Can't say anything for Play since I haven't used that, but if you face growth problems with your Grails project (scaling), just piece off the heavy parts and create separate services written in Scala. First hand experience, Finagle is a good choice for this. You can easily be productive and quickly create services with this RPC system.
Conclusion: In my opinion, your best option for creating an MVP/Prototype is Grails.