Well there is some workarround but needs quite an effort. You need to have second PC or good PC to handle streaming and virtual machine. On virtual machine/second PC you setup linux (Debian, Ubuntu, whatever) and install nginx server. On nginx you setup RTMP protocol and then you fork the stream. One stream goes to target server (youtube, twitch, liveleak etc) and second one you grab with VLC. I cant say what is the delay but since you streaming locally (same pc or LAN) it shouldnt be large. All depends how fast nginx handle the stream.
But I didnt do it because it seems too much effort for result - im not desperated so much. Here is step by step guide if you are still interested.
https://www.youtube.com/watch?v=-YGzkD1Su7Q
//EDIT
Remember that OBS Studio has thing like "Media Source". You can setup a separate scene for particular movie, put there your Media Source, set your video with audio and play it when you switch the scene. It still lacks some feature like XSplit - play queue or playing particular part of video, but still is much comfortable than manual playing with external video players.