there is no limit to how much video you can upload, apart from disk space on the server. There is also a limit on how big each file can be according to your PHP configuration, but on on the combined size of all the videos.
Your challenges in this project will be preparing the videos for online viewing (I'd go for mp4-files using h.264 and aac audio).
If you expect huge traffic, I'd consider using Cloudfront for serving the videos.
Also, your server should not be busy with converting and preparing these videos. Perhaps you should consider converting them before you upload them.
Alternatively, you need to look into scaling that part of your site either by using a third party transcoding service or rolling your own.
I'm sure you can find a plugin that handles file uploads via FTP, or makes it possible to download files FROM your FTP server TO your WordPress installation.