I have been using Paperpile with a Chromebook ever since the beta of Paperpile was launched. No problems whatsoever. The only issue that you will have is that the PDFs are not synced with the local storage - and indeed the size of my library (over 8k PDFs) would begin to swamp the limited SSD storage on a Chromebook if it did.
Indeed I am so happy with Chromebooks solution that I have been ditching Mac's and Linux boxes in my research group to move ChromeOS everywhere with Virtual Machines for heavy lifting and Virtual Desktops for any tasks that have not yet migrated to ChromeOS