Dropbox just watches a local directory for changes. The only issue would be two copies of anything (Matlab, Excel, etc.) accessing the same file. Each will see the copy of the file as they opened it. Most likely, after each releases the file, DB will sync it. So whoever wrote last will get the changes propagated.
Re; office365. Just map your shared space as a network drive in Windows.
Better yet, use a version control system like subversion or git to keep your code synced across computers and to handle conflicts. There are online providers for those that take seconds to setup.