Yes, you can store MAXQDA projects in a cloud service like Dropbox, Google Drive, Microsoft OneDrive or SugarSync, to synchronise project files across different computers or to make them available to third parties.
We strongly recommend against working with a project from within the synchronized storage area, meaning that you should never open a project file directly from the cloud folder (e.g. your Dropbox folder). Instead, we recommend copying the project to a location that is not synchronized, e.g. to your desktop, and then copying it back to your cloud service when you have finished working on it.
We cannot guarantee that project files will not be damaged by your cloud service beginning a synchronisation process while your MAXQDA project is open, which may corrupt the project.