“It’s like a Priest teaching at a Jewish School.”
A Priest well steeped in the Old Testament could teach in a Jewish School.
I don't think so.
There's more to the Torah and Jewish Teaching than the Christian Bible's Old Testament.
There are the 'Mosaic Laws' (Laws of Moses), there's over 600 of them that Jews are taught on how to live. And Christians, or a Priest know nothing about them, not having studied them.
No, I don't think a Priest would work.