I was really wanting to build a Raspberry Pi Linux Cluster (~20GB RAM, etc). I was wondering if it would be possible to render video from Adobe Premiere Pro to Linux and how I would incorporate a rendering farm to split up the tasks. Thanks for all of your help!
At the moment, Adobe Premiere Pro struggles to run properly on the systems it supports--Windows 10 and Mac OS 10.10. As of today, Adobe does not even recommend running it on Mac OS 10.11! Premiere Pro does not run at all on Linux, and while you might be able to create some virtualized environment that can host a cluster of OSX or Windows instances on a Linux cluster, such virtualized environments are weakest where Premiere Pro needs them to be strongest: at the CPU/GPU interface. In summary, not today, and likely not in the near future.
A far better starting place for your cluster project would be to select an open source video editor (here's a snapshot of the state of the art for 2015) and evaluate what sort of Raspberry Pi cluster is needed to compete with a typical modern GPU.