Absolutely--you can use the same API without modification to write a web, Android, or Mac client.
Is there any examples out there on how to integrate it with a web-app as well?
What's the big advantage in relation to Parse? I love Heroku, but Parse seems like a really smooth solution for iOS/Mac.
This screencast was merely a demonstration of what a rapid iOS development workflow with the Core Data Buildpack looks like.
This looks better for getting started quickly if you have a Core Data app. It should also be easier to customise although Parse can do more for you (user registration is built in) but you need to be on the paid ($199/month) package to use your own branded login I think.
Also I can't quite tell but it might be possible to take the Heroku buildpack and deploy it on your own servers so i think you would have easier options to migrate away without a rebuild. This is worth something to me.