Can users edit their form submissions?

I'm using wordpress to manage a user account area. I've already got a registration process set up. Only users will be able to see and submit forms.

I want a form that only users can submit (with certain fields populated from their user data (at least user ID)), and, ideally I'd like users to be able to view forms they've submitted and view or update their submissions as necessary. I'd also like to keep submissions to 1 submission per user.

Is this supported?

I am a programmer, so I can integrate with the API as necessary, but I'd love an idea of how easy this is to integrate with the existing GF model...

Thanks for the quick reply! This seems reasonable. Can users view their submissions perchance? Or is there a simple API hook / permission to allow them to view their submissions?