She might find out about the tape. Or she might not. It is not guaranteed, but she will know for sure if you tell her.
You'd be effectively kicking her down while she's at her lowest, as opposed to theoretical possibility of Sage finding out at some point down the road, when she's feeling better. I really don't think telling her now is in any way more beneficial for her.
If either Jade or Stephen want for some reason to inform Sage that her adoptive mother fucks her students, well, that's on them.