Amazon EC2 Nginx to S3

Currently I'm setting up Amazon EC2 Server with Nginx + RTMP. I'm creating live stream server and I want to record every live stream video and stored in my server. Now I can stored my live stream video to Amazon EC2 VPS linux server. Is it a good ideas to store all the recorded video files in linux server ? I want to use Amazon CDN so I need Amazon S3.

Can I stored directly to S3 after live streaming video ?

rtmp {
        server {
                listen 1935;
                chunk_size 4096;

                application live {
                        live on;
                        record all;
                        record_path /home/ubuntu/mnt;
                }
        }
}