Hello -
I wanted to give a more definitive answer to this report. It does appear that syncing a project with Dropbox will cause a crash when your Editor is attempting to write to the Intermediate folder, which usually happens when compiling shaders, opening maps etc.
It does look like in UE-17227 which was fixed in time for the 4.10 release, an attempt to harden the engine against this type of crash was put in place. A brief attempt with Antidamage’s project was made in 4.10 using Dropbox and did not experience a crash. This will work for a large percentage of people with this issue, but may not fix every single one.
My biggest suggestion is not to use Cloud storage (Dropbox, Google Drive, OneDrive, etc.) directly with your whole project directory. If you do make sure that you manually control syncing and do not try to sync while also working on the same project files.
Thank You
Eric Ketchum