Yes, it is possible to store MAXQDA projects in a cloud service like Dropbox, Google Drive or SugarSnyc, to synchronise project files across different computers or to make them available to third parties.
We strongly recommend that you do not work with a project inside the synchronized storage area, meaning that you never open a project file from right within the cloud folder (e.g. your Dropbox folder). Instead, we recommend to copy the project to a location that is not synchronized e.g. to your desktop and copy it back to your cloud service when you are finished working on it.
Especially when working on a Mac computer we cannot guarantee that project files are damaged by your cloud service starting a synchronisation process while the MAXQDA project is opened, thus possibly corrupting the project.