Many, many streamers have been getting away with streaming copyrighted music for a while now, by simply not recording VODs (or, recording them in such a way that the music is excluded).
My understanding is that this practice is still technically illegal (since live-broadcasting music without recording it is still something you need copyright permission for), but significantly more difficult for record companies to crack down on.
The second-last paragraph seems to cover this. In short, no - but it seems reasonable to believe this could be a solid stepping-stone on the path from here to there.
If you just want background music that won't set off any DMCA alarms use one of the generative AI music tools. Even the examples and 10-second tests are probably good enough (just loop them), LOL
By law they can't be copyrighted since they were generated by AI.
My understanding is that this practice is still technically illegal (since live-broadcasting music without recording it is still something you need copyright permission for), but significantly more difficult for record companies to crack down on.