(Hopefully this post will be edited to answer yes, but right now, it seems that a Google account is necessary to obtain the Discourse App for Android.)
F-Droid is an installable catalogue of FOSS (Free and Open Source Software) applications for the Android platform. The client makes it easy to browse, install, and keep track of updates on your device.
The F-Droid community uses Discourse! Please add the Discourse App for Android to the F-Droid catalogue!