I'll try to clarify some things here:
With Chief Architect Project Management turned on, you cannot directly save plans, layouts, or Projects to DropBox or another cloud service. These files are managed by Chief and stored outside of the typical X17 Data Folder.
What can be saved to DropBoxor another cloud service are exported Project (.caproj) files. Exporting a Project makes a copy of the project files stored within Chief and bundles together all plans, layouts, and referenced asset files used within a Project. You can think of a Project (.caproj) file as equivalent to the output produced by 'Back Up Entire Plan/Layout' in X16 and other previous versions of Chief. Backups--which contain all Projects and their associated files, as well as libraries, preferences, and other settings--can also be stored on a cloud service. You can make a backup at any time using File > Back Up and Restore... > Back Up Managed Resources.... Chief is also set up to create these backups at midnight, by default. Depending on your use case, storing Project files and backups on a cloud service may be sufficient for your needs.
Like @ComputerMaster86said, with Chief Architect Project Management turned off, plans and layouts can be saved to DropBox just like in previous versions. If you work in a highly collaborative environment, this may be the right choice for you.
I would encourage you (and other users) to give Chief Architect Project Management a try and see if it is compatible with your workflow. If it doesn't, turning Project Management off allows you to manage files just like previous versions.