Yes you can use a ftp client on your web server (in a net app), however not on the client page itself.
Keep in mind that when you are uploading large files from a web page, that you have to wait until the entire file is uploaded to the server, before you can do anything with it, even check its size. Also this file will be on the server memory, which if you are having a lot of large files uplaoded, may exceed your memory limit on server.
The way around this is to intercept the http request.begin event in a http module, and chunk the file to disk. Then you can also monitor the progress of the upload.
Why would this not work with apple OS, can they not display an .aspx page, which for a browser client is just plain html. You only need a net server to host it on.
You can upload multiple files at once.
It is a lot of work writing the code to do all of this, and the easiest solution may be to use one of thethird party solutions.