Depends... you have 2 options...

1.) Script downloads the requested file to your server before serving it to the end-user.
2.) Script streams the file to the end user without downloading (but through the server).

In both cases, you'll use a lot of bandwidth, and possibly lots of resources (Because of a lot of consistent open HTTPD connections [rs link generators get popular in a very short time]).

But in case 1, you'd need adequate disk space for temporary file storage. In case 2, none (except a couple MB) would be required.