Wow, I actually have that kit.  Don’t use it much anymore, but it worked quite well.  Unfortunately, I used it with playbar so, the connections are going to be different.

Anyway, I don’t think it will work as you expect it to.  Yes, the mixer can take in an HDMI-ARC signal from your TV, but it does not appear to have a way to pass that ARC signal on to the Sonos Arc. If you watch the video, you’ll see they don’t have a second HDMI cable connected to the mixer, they use the aux audio cable. 

On the US version of Amazon page they show that you can connect by source → mixer → TV, and this is the way that I would do it. You can then leave your Sonos Arc connected to the TV as normal.

If I remember, and can find the mixer, I may try and connect it to verify this works.