Heroku's GitHub sync features are hard-coded to connect to and use github.com. GitHub Enterprise comes in two flavors: Enterprise Server and Enterprise Cloud.
Enterprise Cloud
GitHub Enterprise Cloud is hosted at github.com. There should be no issues in integrating an Enterprise Cloud organization at github.com/organization with Heroku.
Enterprise Server
It is possible to manage this process with a deployment web service of your own that receives webhooks from your GitHub Enterprise service, and can then retrieve the repository's sources and pushes them to the relevant Heroku application. This would also maintain a higher level of security as the contents would only leave your infrastructure when being sent to Heroku, which also only happens over secure channels.