Hello,
Apple is the only one who can answer acceptance questions for sure, and they can also change their criteria at any time, but there are many developers using OpenEars in the background and I don’t know of any rejections. It seems like it is in line with Apple’s definition of an audio app.
And what about the microphone permissions?
I’d say you’d need to get permissions in the foreground and indicate commencing listening in the foreground before going into the background.