However, from a legal standpoint, it is acceptable if copyrighted music/material is playing in the background of a video/slive stream and is captured if the videographer would have no reasonable way of blocking out said background/ambient music/material.
But, of course that would not apply since this isn't a case where you have "no reasonable way of blocking it out". The only reason the music would be in your video is that you are intentionally playing it in an attempt the skirt the copyright law. This thread could be exhibit one in the copyright holder's lawsuit!