Is there a way of downloading a file to an online storage area from another site without downloading to the terminal first

The quick answer is Yes, their are multiple ways to do this. If you have a website that is hosted, you should be able to download to the server, as long as you have the proper login information. A pseudo way to have all of your downloads 'saved' to the online drive would be to tell your browser to save the file to the other drive, you still need the proper login information.
If you are an Apple user, the '.Mac'(dot Mac) service would be helpful to you.

If you have the ability to login remotely to the online storage area you are using, you could also go that route.

Hope this has helped, some other resources for you to visit:
TechRepublic.com Or Leafnetworks.net

cheers/rc