Yes, but it will involve some significant software development work.
When a file is uploaded to DreamObjects and set to NOT have public-read access permissions, you can allow a user to download the file by giving them a "signed" URL. The signature on this URL can contain an expiration date, so that it doesn't last forever.
Probably the easiest way (and I use this term loosely) of going about this would be to get started with the Amazon Web Services SDK for PHP. The S3 component of this library is compatible with DreamObjects, with the exception of a few oddball features we haven't implemented yet (like BitTorrent downloads). Example code for using this library with DreamObjects is available on docs.dreamobjects.net.
The tricky part, of course, will be integrating this with Joomla. This part I have little familiarity with.