Thinking about this a little more, the potential security risks are much higher, as well the practicalities of offering such a specific service may undemine what is trying to be achieved. As Mary has suggested, in v1.9.x the site files are wide open to anyone who can guess the URL could, potentially, wreck both the uploads and downloads. (As most damaging cracks are made by someone trusted, who is already past the firewall with legitimate access, even forcing users to login may not safeguard the site.)
I read it to mean that the User would be able to use the Moodle itself, essentially, as a repository. You are asking if Users are be enabled to push, upload, completed assignments to a specific point, and pull, download, new assignments from a different point. Moodle does this already, in a formalized course structure. I take it you are asking for a simpler method than this formal course structure to be able to upload and download.
I am sure someone could work it out, but how it could be done without compromising site security, or risking confidentiality, or maintaining the integrity of the User uploads, (I mean ensuring the person uplaoding is really the person who should be uploading), is beyond me. I think probably not really worth the effort to pursue it - the risks are higher than the gains.
One potential way around this is using the course structire and that only consists of downloadable assignments, titled properly, of course, and those assignments have uploadable responses, either single or multiple files types. Stll need courses, but they have nothing but assingments in them.
