Some programs can do that. MS Office, for example, can save straight to Sharepoint locations, together with full blown tree browsing.
Some network file exchange protocols are available in Windows (Linux, MacOS) as redirectors. That means that they present themselves to the userland programs as ordinary filesystems. SMB/CIFS is the prime example, although probably no one uses SMB over Internet as-is. FTP, even though folder browsing is supported in Explorer alongside regular folders, is not a filesystem. Sometimes you can channel SMB over Internet via an encrypted channel, like a VPN or SSH - this requires control over both client and server.
Some cloud storages expose an API that a program could use to browse to and save directly to the cloud. Dropbox and Google Drive work that way. Anyone can write a program that saves/loads to Dropbox, or browses files on Dropbox. But it has to be done explicitly - you're targeting Dropbox, not just any cloud storage.
Dropbox also provides a store-and-forward solution - you save to a designated local folder which is eventually synced up with Dropbox.
With a generic program (not written to be cloud-aware) and a generic cloud storage (incapable of emulating a filesystem), however, you're out of luck.
For sharing specifically sources over the 'Net, the preferred way to do that is with an online source control system. There are public Subversion repositories out there; most IDEs can talk to those. But the commit to SVN step is usually manual. A local folder is still involved; it's a save-then-upload by other name.
By the way, having your source location in the cloud would be a considerable performance penalty. Internet is fast these days, but still no match for a hard drive.