Because there is no offline mode, downloading PDFs to your local computer is necessary. Currently, some people use google drive’s sync to handle this. There are two issues with that: (1) google drive doesn’t organize papers by paperpile’s subfolders, and (2) on linux there is no official google drive client.
As a result, downloading papers is currently necessary. Paperpile could make this much easier if they allowed local download of multiple papers by shift-selecting them.