No. "She read you a book" is "Σου/Σας διάβασε ένα βιβλίο" in modern Greek. :-)
σας is "your" when it is after a definite noun, as in το βιβλίο σας "your book".
But here, σας is not after a noun but instead before the verb -- "(to) you".
Because the speaker is speaking to several people at once, or perhaps speaking to someone they do not know very well.
σου is the informal singular, σας is the informal plural but is also used as the formal pronoun (singular or plural). Like French tu/vous if you're familiar with that.