I know that I need the synchronize box for it but do you think the box can use the emulated Hue bridge from OH to du the synchronization with the lights?
The very simple answer is NO. The hue sync box scans the video data and matches that to the colours needed by the lamps/bulbs. The hue emulation binding is to present none hue things as if they were, thus being able to control say an X10 thing using a voice assistant.
There are a few alternatives to the hue sync box, but most of them use an image sensor rather than the HDMI data and therefore not that great.
The nearest your going to get is to create a script/rule that randomises the colours when your TV is turned on, or maybe when you have a movie playing.
I have limited knowledge and hopefully someone more knowledgeable will turn up soon and add more information