Here is a concept regarding your query.
It is possible and the toolchain with GitHub and Delivery Pipeline integrations can solve problems just like this. You can even have the toolchain build and publish the application to Bluemix automatically when you push to your GitHub repository.
You can view the toolchain docs
or you can create a toolchain from a template to help you get started and play around with the Delivery Pipeline integration to build your packaged server.
I have an example toolchain
Click Create Toolchain button at the bottom that may be helpful for you to create and poke around with as it includes a toolchain with GitHub and delivery pipeline integrations to build a liberty app with a packaged server. It also pushes it to Bluemix.
I hope the above information will be helpful for you.