No Way In Hell.

As a programmer, I'll give my less-than-humble opinion that such a program would be unbelievably difficult to write, and as such, not worth it.

It would be difficult because some of the things that all modern operating systems provide for us (that we take for granted) are not supported in DOS. Like:

Memory management- getting at the memory above 640k is a pain, and this app would need several megs to manage its data. Not impossible to deal with, but...

"Sockets" - a socket is the connection your computer opens to UL/DL a file or some information. Modern OSes handle connecting with the other computer, send/recv, error control, closing the connection, etc... These would all have to be implemented by hand (compliant with the standard for BSD sockets)...
An effort of Tantalus... but if I HAD to do it, I would copy the Sockets implementation from Linux!! The whole thing, just cut and paste

Anyway... not worth it... But as long as a program runs on Win, Mac, and Linux, it's all good, right??
That's the trend with clients being written in Java (LimeWire), so they don't have to be rewritten across platforms...