As long as all the source is freely available, and all the libraries that it uses are free software, it should be just a matter of getting it to build. The GPLv3 and Apache-2.0 license have similar patent clauses. I think most free software people are opposed to software patents.
There is a good chance that this app uses the proprietary Google Play Services GMS libraries, for example, GCM. Lots of realtime communications apps do.
As for the build, the process is literally like running a shell script in a Debian/jessie machine with the whole Android SDK setup. If the packages you need are missing, you could download them as part of the build recipe.