I know the battery box doesn't amplify.
But I also know that for many years I have been going Mic-->Battery Box-->Line-in at any show with a PA system--and some, like orchestras, without.
People who, unlike me, actually know something about electronics and work with professional equipment are used to sending a pre-amped signal into Line-in. All I can say is, battery box into Line-in works. Maybe it's because I've always been using Sony recorders and plug-in-power mics, but it works.