No, you can not upload files using Safari, with any website. The iPad does not maintain a general file space, so there is no where to look when the websites give you the Choose File option.
There are a few way around it.
One, as you notices you can upload using the FaceBook app. There are other third party FaceBook apps that have similar options. Some members prefer these, and they may have better upload options. Search the site for favorite FaceBook apps.
iCab Mobile can upload to some (most) sites. It is a third party web browser that creates its own file space for uploads. Most file types have to copied to iCab (using the Open In feature, usually) before they can be uploaded; pictures however can be uploaded directly from the Photos library.
