Can you render Adobe Premiere or After Effects projects on Linux using a render manager?
No. Unfortunately Adobe only supports win or osx. Official forum post about Deadline:


  Deadline itself is a cross-platform application, but it can only render on  operating systems that the rendering software itself supports. So AE and  C4D will only work on Windows and OSX.


Also see the manual: http://docs.thinkboxsoftware.com/products/deadline/7.1/1_User%20Manual/



Thus it depends on the main application, if you are able to build a render farm on linux. In the case of adobe, the only remaining option is using a Virtual Machine for now.