I have been using it for a about a year. I love the workflow that it provides but I find not having access to the data is a real bother. Your options for working with database are:
Taps: In theory you create your database however you want locally and use taps to copy both schema and data to Heroku. In practice, most of the time its amazingly great. However I am currently dealing with the cleanup after taps translated some of my columns poorly and corrupted my data.
Heroku console: Totally fine for all the usual ActiveRecord stuff, but closest you can get to the database is ActiveRecord::Base.connection.execute "some sql". When you find yourself wondering about doing alter table commands like that you will know you're in trouble.
They also provide a "bundle" as a method for backing up your app. This lets you download all your code plus a sql dump of the database. The difficulty is that since there is no direct database access there is no way of loading that same sql dump back into the database so you can recover from dataloss, which, to me, is the point of having those dump files to begin with. All you can use the bundle for is to create a new application (heroku bundles:animate), not restore a current app.
I would love to be wrong about any/all of these. This seems like a curious rough spot in the best thought out service that I know of. Database access normally doesn't feel like much to give up when most of what you do is made so easy.
To me database access is like a fire extinguisher. Usually not a big deal, but when it matters, it matters a lot.